Dynamically ordered energy function for Morse-Smale diffeomorphisms on 3-manifolds
Geometric Topology
2012-10-18 v2
Abstract
This note deals with arbitrary Morse-Smale diffeomorphisms in dimension 3 and extends ideas from \cite{GrLaPo}, \cite{GrLaPo1}, where gradient-like case was considered. We introduce a kind of Morse-Lyapunov function, called dynamically ordered, which fits well dynamics of diffeomorphism. The paper is devoted to finding conditions to the existence of such an energy function, that is, a function whose set of critical points coincides with the non-wandering set of the considered diffeomorphism. We show that the necessary and sufficient conditions to the existence of a dynamically ordered energy function reduces to the type of embedding of one-dimensional attractors and repellers of a given Morse-Smale diffeomorphism on a closed 3-manifold.
Keywords
Cite
@article{arxiv.1101.6036,
title = {Dynamically ordered energy function for Morse-Smale diffeomorphisms on 3-manifolds},
author = {Viatcheslav Grines and Francois Laudenbach and Olga Pochinka},
journal= {arXiv preprint arXiv:1101.6036},
year = {2012}
}