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

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In this paper, we utilize the sub-additive unstable topological pressure to give an upper bound for the upper box dimension of the C1 hyperbolic set on local unstable manifold. As a by-product, we give a new expression of the topological pressure on symbolic spaces. This work is inspired by Barreira (1996), Feng and Simon (2023) and Zhang et al. (2022).