Fixed point indices of iterates of orientation-reversing homeomorphisms

2024/09/13 by Grzegorz Graff, Graff, Grzegorz, Patryk Topór +1 · 1 citation
Mathematics · #55M20 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Equations Stability Results #Primary 37B30 #Secondary 37E30

paper · pdf · doi:10.48550/arxiv.2409.08753

openalex publication_date 2024/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that any sequence of integers satisfying necessary Dold's congruences is realized as the sequence of fixed point indices of the iterates of an orientation-reversing homeomorphism of ℝ^m for m≥ 3. As an element of the construction of the above homeomorphism, we consider the class of boundary-preserving homeomorphisms of ℝ^m₊ and give the answer to [Problem 10.2, Topol. Methods Nonlinear Anal. 50 (2017), 643 - 667] providing a complete description of the forms of fixed point indices for this class of maps.

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