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

Congcong Qu

Published 2023-06-24Version 1

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}.