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arXiv · 2107.03493

Geometric Structure and Ergodic Properties of Bony Multi-Graphs

M. Rabiee·F. H. Ghane·M. Zaj
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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.

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M. Rabiee, F. H. Ghane, M. Zaj. 2021-07-07. Geometric Structure and Ergodic Properties of Bony Multi-Graphs. https://arxiv.org/abs/2107.03493

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