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arXiv · 2409.08753

Fixed point indices of iterates of orientation-reversing homeomorphisms

Grzegorz Graff·Patryk Topór
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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 $\mathbb{R}^{m}$ for $m\geq 3$. As an element of the construction of the above homeomorphism, we consider the class of boundary-preserving homeomorphisms of $\mathbb{R}^{m}_{+}$ 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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Grzegorz Graff, Patryk Topór. 2024-09-13. Fixed point indices of iterates of orientation-reversing homeomorphisms. https://arxiv.org/abs/2409.08753

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