Finding periodic points of a map by use of a \(k\)-adic expansion

DOI10.3934/dcds.1999.5.495zbMath0965.37015OpenAlexW2005037441MaRDI QIDQ1576849

Wacław Marzantowicz, Piotr Maciej Przygodzki

Publication date: 16 August 2000

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.1999.5.495

zbMATH Keywords

periodic pointsLefschetz number\(k\)-adic expansioniteration of map

Mathematics Subject Classification ID

Fixed points and coincidences in algebraic topology (55M20) Index theory for dynamical systems, Morse-Conley indices (37B30) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Related Items (13)

On partially periodic point free self-maps on the wedge sums of spheres ⋮ Local fixed point indices of iterations of planar maps ⋮ Fixed point indices of iterated smooth maps in arbitrary dimension ⋮ General form of fixed point indices of an iteratedC¹map and infiniteness of minimal periods ⋮ Generating sequences of Lefschetz numbers of iterates ⋮ Periodic expansion in determining minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms ⋮ Algebraic periods of self-maps of a rational exterior space of rank 2 ⋮ Indices of iterations and periodic points of simplicial maps of smooth type. ⋮ The Nielsen and Reidemeister numbers of maps on infra-solvmanifolds of type \((\mathrm{R})\) ⋮ Minimal number of periodic points for C 1 self-maps of compact simply-connected manifolds ⋮ Periodic segment implies infinitely many periodic solutions ⋮ Dold sequences, periodic points, and dynamics ⋮ Periodic points of multivalued mappings with applications to differential inclusions on tori.

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