An upper bound for the box dimension of the hyperbolic dynamics via unstable pressure

Congcong Qu

doi:10.1016/j.na.2024.113560

paper

An upper bound for the box dimension of the hyperbolic dynamics via unstable pressure

arXiv:2306.13898 · doi:10.1016/j.na.2024.113560

Abstract

In this paper, we utilize the sub-additive unstable pressure to give an upper bound for the upper box dimension of the $C^{1}$ hyperbolic set on unstable manifolds. As a by-product, we give a new expression of the topological pressure. This work is inspired by \cite{FS, WCZ, CliPZ}.