Geometric Structure and Ergodic Properties of Bony Multi-Graphs
Dynamical Systems
2021-07-09 v1
Abstract
The main goal in this paper is to describe the geometric structure of invariant graphs of a certain class of skew products. Our focus is on attracting multi-graphs. An invariant multi-graph is an invariant compact set which is a finite union of invariant graphs, and thus consists of a finite number of points on each fiber. We introduce invariant bony multi-graphs and construct an open set of skew products over an invertible base map (solenoid map) having attracting invariant multi-graphs and bony multi-graphs which support finitely many ergodic SRB measures. In this study some thermodynamic properties are investigated. Finally, we extend our results to a family of skew products over a generalized baker map.
Keywords
Cite
@article{arxiv.2107.03493,
title = {Geometric Structure and Ergodic Properties of Bony Multi-Graphs},
author = {M. Rabiee and F. H. Ghane and M. Zaj},
journal= {arXiv preprint arXiv:2107.03493},
year = {2021}
}
Comments
23 pages, 1 figure