Existence of an energy function for 3-dimensional chaotic "sink-source" cascades
Dynamical Systems
2021-06-30 v2
Abstract
The paper is a continuation of research in the direction of energy function (a smooth Lyapunov function whose set of critical points coincides with the chain recurrent set of a system) construction for discrete dynamical systems. The authors established the existence of an energy function for any -diffeomorphism of a three-dimensional closed orientable manifold whose non-wandering set consists of chaotic one-dimensional attractor and repeller.
Keywords
Cite
@article{arxiv.2009.10457,
title = {Existence of an energy function for 3-dimensional chaotic "sink-source" cascades},
author = {M. Barinova and V. Grines and O. Pochinka and B. Yu},
journal= {arXiv preprint arXiv:2009.10457},
year = {2021}
}
Comments
21 pages, 9 figures