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Search results for: algebraic periods
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Algebraic periods of self-maps of a rational exterior space of rank 2
PublicationArtykuł stanowi kompletny opis okresów algebraicznych dla odwzorowań wymiernej przestrzeni zewnętrznej rangi 2 w siebie.
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Algebraic periods and minimal number of periodic points for smooth self-maps of 1-connected 4-manifolds with definite intersection forms
PublicationLet M be a closed 1-connected smooth 4-manifolds, and let r be a non-negative integer. We study the problem of finding minimal number of r-periodic points in the smooth homotopy class of a given map f: M-->M. This task is related to determining a topological invariant D^4_r[f], defined in Graff and Jezierski (Forum Math 21(3):491–509, 2009), expressed in terms of Lefschetz numbers of iterations and local fixed point indices of...
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Database of algebraic periods of quasi-unipotent orientation-preserving homeomorphisms of orientable surfaces
Open Research DataThe set of algebraic periods of a map contains important information about periodic points and, in addition, is a homotopy invariant of the map. It is determined by indices of nonzero Dold coefficients which are computed purely algebraically from maps induced on homology groups of a considered space. In this dataset, we include for a given g=1,2,...,30,...
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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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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...