On existence of a Morse energy function for topological flows with finite chain recurrent sets
Dynamical Systems
2019-04-18 v1
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.
Cite
@article{arxiv.1904.08086,
title = {On existence of a Morse energy function for topological flows with finite chain recurrent sets},
author = {Timur V. Medvedev and Olga V. Pochinka and Svetlana Kh. Zinina},
journal= {arXiv preprint arXiv:1904.08086},
year = {2019}
}