Local weighted topological pressure

TL;DR

This paper introduces the concept of local weighted topological pressure and extends existing variational principles to this localized setting, enhancing the understanding of weighted topological dynamics.

Contribution

It generalizes the variational principle for weighted topological pressure to a local context, building on Feng and Huang's foundational work.

Findings

Established the notion of local weighted topological pressure.

Extended the variational principle to the localized setting.

Provided theoretical framework for future research in weighted topological dynamics.

Abstract

In [D. Feng, W. Huang, Variational principle for weighted topological pressure. J. Math. Pures Appl. (2016)], the authors studied weighted topological pressure and established a variational principle for it. In this paper, we introduce the notion of local weighted topological pressure and generalize Feng and Huang's main results to localized version.