Year 2024

• Algebraic periods and minimal number of periodic points for smooth self-maps of 1-connected 4-manifolds with definite intersection forms

  Publication

  • H. Duan
  • G. Graff
  • J. Jezierski
  • A. Myszkowski

  - Journal of Fixed Point Theory and Applications - Year 2024

  Let 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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Year 2022

• Minimal Sets of Lefschetz Periods for Morse-Smale Diffeomorphisms of a Connected Sum of g Real Projective Planes

  Publication

  • G. Graff
  • A. Myszkowski

  - Year 2022

  The 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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Year 2020

• Computations of the least number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds

  Publication

  • G. Graff
  • J. Jezierski
  • A. Myszkowski

  - Topological Methods in Nonlinear Analysis - Year 2020

  Let $r$ be an odd natural number, $M$ a compact simply-connected smooth manifold, $\dim M\geq 4$, such that its boundary $\partial M$ is also simply-connected. We consider $f$, a $C^1$ self-maps of $M$, preserving $\partial M$. In [G. Graff and J. Jezierski, Geom. Dedicata 187 (2017), 241-258] the smooth Nielsen type periodic number $D_r(f;M,\partial M)$ was defined and proved to be equal to the minimal number of $r$-periodic points...

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Year 2019

• Periodic expansion in determining minimal sets of Lefschetz periods for Morse–Smale diffeomorphisms

  Publication

  • G. Graff
  • M. Lebiedź
  • A. Myszkowski

  - Journal of Fixed Point Theory and Applications - Year 2019

  We 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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