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Search results for: Morse-Smale diffeomorphisms
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Periodic expansion in determining minimal sets of Lefschetz periods for Morse–Smale diffeomorphisms
PublicationWe apply the representation of Lefschetz numbers of iterates in the form of periodic expansion to determine the minimal sets of Lefschetz periods of Morse–Smale diffeomorphisms. Applying this approach we present an algorithmic method of finding the family of minimal sets of Lefschetz periods for Ng, a non-orientable compact surfaces without boundary of genus g. We also partially confirm the conjecture of Llibre and Sirvent (J Diff...
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Minimal Sets of Lefschetz Periods for Morse-Smale Diffeomorphisms of a Connected Sum of g Real Projective Planes
PublicationThe dataset titled Database of the minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms of a connected sum of g real projective planes contains all of the values of the topological invariant called the minimal set of Lefschetz periods, computed for Morse-Smale diffeomorphisms of a non-orientable compact surface without boundary of genus g (i.e. a connected sum of g real projective planes), where g varies from 1 to...
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Database of the minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms of a connected sum of g tori
Open Research DataMorse–Smale diffeomorphisms, structurally stable and having relatively simple dynamics, constitute an important subclass of diffeomorphisms that have been carefully studied during past decades. For a given Morse–Smale diffeomorphism one can consider “Minimal set of Lefschetz periods”, which provides the information about the set of periodic points of...
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Database of the minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms of a connected sum of g real projective planes.
Open Research DataMorse–Smale diffeomorphisms, structurally stable and having relatively simple dynamics, constitute an important subclass of diffeomorphisms that were carefully studied during past decades. For a given Morse–Smale diffeomorphism one can consider “Minimal set of Lefschetz periods”, which provides the information about the set of periodic points of considered...
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The database of odd algebraic periods for quasi-unipotent self-maps of a space having the same homology group as the connected sum of g tori
Open Research DataThe dataset consists of 20 files indexed by numbers g=1,...,20. Each file provides sets of odd algebraic periods for all quasi-unipotent self-maps of a space having the same homology groups as the connected sum of g tori. Let us remark that each data set covers all algebraical restrictions that come from zeta functions for the sets of minimal Lefschetz...
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Equivariant Morse equation
PublicationThe paper is concerned with the Morse equation for flows in a representation of a compact Lie group. As a consequence of this equation we give a relationship between the equivariant Conley index of an isolated invariant set of the flow given by x˙ = − ∇f(x) and the gradient equivariant degree of ∇f. Some multiplicity results are also presented.
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Index filtrations and Morse decomposition for discrete dynamical systems
PublicationOn a Morse decomposition of an isolated invariant set of a homeomorphism(discrete dynamical system) there are partial orderings defined by the homeomorphism.These are called admissible orderings of the...
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Morse inequalities via Conley index theory
PublicationThe relation known as the Morse inequalities can be extended to a more general setting of flows on a locally compact metric spaces (Conley index) as well as dynamical systems on Hilbert spaces (LS-index). This paper is a discourse around this extension. Except the part concerning the LS-index the material is self-contained and has a character of a survey.
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Morse cohomology in a Hilbert space via the Conley index
PublicationThe main theorem of this paper states that Morse cohomology groups in a Hilbert space are isomorphic to the cohomological Conley index. It is also shown that calculating the cohomological Conley index does not require finite-dimensional approximations of the vector field. Further directions are discussed.
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Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces
PublicationIn this paper we introduce a new compactness condition — Property-(C) — for flows in (not necessary locally compact) metric spaces. For such flows a Conley type theory can be developed. For example (regular) index pairs always exist for Property-(C) flows and a Conley index can be defined. An important class of flows satisfying the this compactness condition are LS-flows. We apply E-cohomology to index pairs of LS-flows and obtain...
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The Palais–Smale condition for the Hamiltonian action on a mixed regularity space of loops in cotangent bundles and applications
PublicationWe show that the Hamiltonian action satisfies the Palais-Smale condition over a “mixed regular- ity” space of loops in cotangent bundles, namely the space of loops with regularity H^s, s ∈ (1/2, 1), in the baseand H^{1−s} in the fiber direction. As an application, we give a simplified proof of a theorem of Hofer-Viterbo on the existence of closed characteristic leaves for certain contact type hypersufaces in cotangent bundles.
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Index filtrations and Morse decompositions for discrete dynamical systems
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Morse decompositions for a two-patch vaccination model
Open Research DataThis dataset contains selected results of rigorous numerical computations described in Section 5 of the paper "Rich bifurcation structure in a two-patch vaccination model" by D.H. Knipl, P. Pilarczyk, G. Röst, published in SIAM Journal on Applied Dynamical Systems (SIADS), Vol. 14, No. 2 (2015), pp. 980–1017, doi: 10.1137/140993934.
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Vector Field Editing and Periodic Orbit Extraction Using Morse Decomposition
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Morse decompositions for a two-dimensional discrete neuron model (low resolution)
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper “Topological-numerical analysis of a two-dimensional discrete neuron model” by Paweł Pilarczyk, Justyna Signerska-Rynkowska and Grzegorz Graff. A preprint of this paper is available at https://doi.org/10.48550/arXiv.2209.03443.
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Morse decompositions for a two-dimensional discrete neuron model (limited range)
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper “Topological-numerical analysis of a two-dimensional discrete neuron model” by Paweł Pilarczyk, Justyna Signerska-Rynkowska and Grzegorz Graff. A preprint of this paper is available at https://doi.org/10.48550/arXiv.2209.03443.
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Morse decompositions for a two-dimensional discrete neuron model (full range)
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper “Topological-numerical analysis of a two-dimensional discrete neuron model” by Paweł Pilarczyk, Justyna Signerska-Rynkowska and Grzegorz Graff. A preprint of this paper is available at https://doi.org/10.48550/arXiv.2209.03443.
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Conley-Morse graphs for a two-patch vaccination model
Open Research DataThis dataset contains selected results of rigorous numerical computations described in Section 5 of the paper "Rich bifurcation structure in a two-patch vaccination model" by D.H. Knipl, P. Pilarczyk, G. Röst, published in SIAM Journal on Applied Dynamical Systems (SIADS), Vol. 14, No. 2 (2015), pp. 980–1017, doi: 10.1137/140993934.
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Morse decompositions for a non-linear Leslie population model with 2 varying parameters
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "A database schema for the analysis of global dynamics of multiparameter systems" by Z. Arai, W. Kalies, H. Kokubu, K. Mischaikow, H. Oka, P. Pilarczyk, published in SIAM Journal on Applied Dynamical Systems (SIADS),...
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Morse decompositions for a non-linear Leslie population model with 3 varying parameters
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "A database schema for the analysis of global dynamics of multiparameter systems" by Z. Arai, W. Kalies, H. Kokubu, K. Mischaikow, H. Oka, P. Pilarczyk, published in SIAM Journal on Applied Dynamical Systems (SIADS),...
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Recurrence times in the Morse sets for a two-dimensional discrete neuron model (low resolution)
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper “Topological-numerical analysis of a two-dimensional discrete neuron model” by Paweł Pilarczyk, Justyna Signerska-Rynkowska and Grzegorz Graff. A preprint of this paper is available at https://doi.org/10.48550/arXiv.2209.03443.
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Conley-Morse graphs for a two-dimensional discrete neuron model (low resolution)
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper “Topological-numerical analysis of a two-dimensional discrete neuron model” by Paweł Pilarczyk, Justyna Signerska-Rynkowska and Grzegorz Graff. A preprint of this paper is available at https://doi.org/10.48550/arXiv.2209.03443.
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Conley-Morse graphs for a two-dimensional discrete neuron model (limited range)
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper “Topological-numerical analysis of a two-dimensional discrete neuron model” by Paweł Pilarczyk, Justyna Signerska-Rynkowska and Grzegorz Graff. A preprint of this paper is available at https://doi.org/10.48550/arXiv.2209.03443.
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Conley-Morse graphs for a two-dimensional discrete neuron model (full range)
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper “Topological-numerical analysis of a two-dimensional discrete neuron model” by Paweł Pilarczyk, Justyna Signerska-Rynkowska and Grzegorz Graff. A preprint of this paper is available at https://doi.org/10.48550/arXiv.2209.03443.
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Conley-Morse graphs for a non-linear Leslie population model with 2 varying parameters
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "A database schema for the analysis of global dynamics of multiparameter systems" by Z. Arai, W. Kalies, H. Kokubu, K. Mischaikow, H. Oka, P. Pilarczyk, published in SIAM Journal on Applied Dynamical Systems (SIADS),...
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Conley-Morse graphs for a non-linear Leslie population model with 3 varying parameters
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "A database schema for the analysis of global dynamics of multiparameter systems" by Z. Arai, W. Kalies, H. Kokubu, K. Mischaikow, H. Oka, P. Pilarczyk, published in SIAM Journal on Applied Dynamical Systems (SIADS),...
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QSAR, QSPR and QSRR in Terms of 3-D-MoRSE Descriptors for In Silico Screening of Clofibric Acid Analogues
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Morse decompositions for a population model with harvesting. Case He-Se: Equal harvesting and equal survival rates of juveniles and adults
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Morse decompositions for a population model with harvesting. Case Ha-Se: Harvesting adults only, equal survival rates of juveniles and adults
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Morse decompositions for a population model with harvesting. Case Hj-Se: Harvesting juveniles only, equal survival rates of juveniles and adults
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Morse decompositions for a population model with harvesting. Case Ha-S1: Harvesting adults only, survival rates of juveniles and adults add up to 1
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Morse decompositions for a population model with harvesting. Case Hj-S1: Harvesting juveniles only, survival rates of juveniles and adults add up to 1
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Morse decompositions for a population model with harvesting. Case He-S1: Equal harvesting of juveniles and adults, survival rates of juveniles and adults add up to 1
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Conley-Morse graphs for a population model with harvesting. Case He-Se: Equal harvesting and equal survival rates of juveniles and adults
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Conley-Morse graphs for a population model with harvesting. Case Hj-Se: Harvesting juveniles only, equal survival rates of juveniles and adults
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Conley-Morse graphs for a population model with harvesting. Case Ha-Se: Harvesting adults only, equal survival rates of juveniles and adults
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Conley-Morse graphs for a population model with harvesting. Case Hj-S1: Harvesting juveniles only, survival rates of juveniles and adults add up to 1
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Conley-Morse graphs for a population model with harvesting. Case Ha-S1: Harvesting adults only, survival rates of juveniles and adults add up to 1
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Conley-Morse graphs for a population model with harvesting. Case He-S1: Equal harvesting of juveniles and adults, survival rates of juveniles and adults add up to 1
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Grand Challenges on the Theory of Modeling and Simulation
PublicationModeling & Simulation (M&S) is used in many different fields and has made many significant contributions. As a field in its own right, there have been many advances in methodologies and technologies. In 2002 a workshop was held in Dagstuhl, Germany, to reflect on the grand challenges facing M&S. Ten years on, a series of M& S Grand Challenge activities are marking a decade of progress and are providing an opportunity to reflect...
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MORSE Morse theoretical methods in Hamiltonian dynamics
ProjectsProject realized in Zakład Układów Dynamicznych according to UMO-2016/23/G/ST1/04081 agreement from 2018-01-03
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Distortion in the group of circle homeomorphisms
PublicationLet G be the group PAff+(R/Z) of piecewise affine circle homeomorphisms or the group Diff∞(R/Z) of smooth circle diffeomorphisms. A constructive proof that all irrational rotations are distorted in G is given.
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Connection matrix theory for discrete dynamical systems
PublicationIn [C] and [F1] the connection matrix theory for Morse decomposition is developedin the case of continuous dynamical systems. Our purpose is to study the case of discrete timedynamical systems.
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Inverse shadowing and related measures
PublicationWe study various weaker forms of the inverse shadowing property for discrete dynamical systems on a smooth compact manifold. First, we introduce the so-called ergodic inverse shadowing property (Birkhoff averages of continuous functions along an exact trajectory and the approximating one are close). We demonstrate that this property implies the continuity of the set of invariant measures in the Hausdorff metric. We show that the...
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Note on universal algoritms for learning theory
PublicationW 2001 Cucker i Smale zaproponowali nowe podejście do teorii uczenia się w oparciu o problematykę teorii aproksymacji.W 2005 i 2007 Bivev, Cohen, Dahmen, DeVore i Temlyakov opublikowali dwie prace z teorii uczenia się. W omawianej publikacji uogólniliśmy ich rezultaty jednocześnie upraszczając dowody.
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Topological invariants for equivariant flows: Conley index and degree
PublicationAbout forty years have passed since Charles Conley defined the homotopy index. Thereby, he generalized the ideas that go back to the calculus of variations work of Marston Morse. Within this long time the Conley index has proved to be a valuable tool in nonlinear analysis and dynamical systems. A significant development of applied methods has been observed. Later, the index theory has evolved to cover such areas as discrete dynamical...
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Continuation classes for a non-linear Leslie population model with 3 varying parameters
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "A database schema for the analysis of global dynamics of multiparameter systems" by Z. Arai, W. Kalies, H. Kokubu, K. Mischaikow, H. Oka, P. Pilarczyk, published in SIAM Journal on Applied Dynamical Systems (SIADS),...
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Continuation classes for a non-linear Leslie population model with 2 varying parameters
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "A database schema for the analysis of global dynamics of multiparameter systems" by Z. Arai, W. Kalies, H. Kokubu, K. Mischaikow, H. Oka, P. Pilarczyk, published in SIAM Journal on Applied Dynamical Systems (SIADS),...
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Continuation classes for a two-patch vaccination model
Open Research DataThis dataset contains selected results of rigorous numerical computations described in Section 5 of the paper "Rich bifurcation structure in a two-patch vaccination model" by D.H. Knipl, P. Pilarczyk, G. Röst, published in SIAM Journal on Applied Dynamical Systems (SIADS), Vol. 14, No. 2 (2015), pp. 980–1017, doi: 10.1137/140993934.
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Continuation classes for a population model with harvesting. Case He-S1: Equal harvesting of juveniles and adults, survival rates of juveniles and adults add up to 1
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.