Quasi-energy function for diffeomorphisms with wild separatrices
Geometric Topology
2010-01-18 v1
Abstract
According to Pixton, there are Morse-Smale diffeomorphisms of the 3-sphere which have no energy function, that is a Lyapunov function whose critical points are all periodic points of the diffeomorphism. We introduce the concept of quasi-energy function for a Morse-Smale diffeomorphism as a Lyapunov function with the least number of critical points and construct a quasi-energy function for any diffeomorphism from some class of Morse-Smale diffeomorphisms on the 3-sphere.
Cite
@article{arxiv.0810.4260,
title = {Quasi-energy function for diffeomorphisms with wild separatrices},
author = {Viatcheslav Grines and Francois Laudenbach and Olga Pochinka},
journal= {arXiv preprint arXiv:0810.4260},
year = {2010}
}