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arXiv · 1904.08086

On existence of a Morse energy function for topological flows with finite chain recurrent sets

Timur V. Medvedev·Olga V. Pochinka·Svetlana Kh. Zinina
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Abstract

We prove the existence of a continuous Morse energy function for an arbitrary topological flow with finite hyperbolic (in topological sense) chain recurrent set on a topological manifold of any dimension. This result is a partial solution of the Morse problem of existence of continuous Morse functions on any topological manifolds. Namely, we prove that a topological manifold admits a continuous Morse function if it admits a topological flow with finite hyperbolic chain recurrent set.

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Timur V. Medvedev, Olga V. Pochinka, Svetlana Kh. Zinina. 2019-04-17. On existence of a Morse energy function for topological flows with finite chain recurrent sets. https://arxiv.org/abs/1904.08086

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