α-BS dimension on subsets

doi:10.1007/s43037-025-00478-7

α-BS dimension on subsets

2026-01-04

1

PRE

AI

DOI：10.1007/s43037-025-00478-7

Original

Original request for help

Save

Abstract

En 中文

We aim to investigate the dimension theory of alpha-pressure-like quantities. By means of the Caratheodory-Pesin structure, we define alpha-BS dimension and alpha-Pesin topological pressure on subsets using alpha-Bowen metric d(n)(alpha)(x, y)=max(0 <= i <= n-1) e(alpha i)d(f(i) x, f(i) y), where alpha >= 0. Specifically, we show that alpha-BS dimension and alpha-Pesin topological pressure are related by a Bowen's equation. Inspired by the classical Brin-Katok entropy, we introduce the notion of alpha-local Brin-Katok entropy, and establish a variational principle for alpha-BS dimension on compact subsets in terms of alpha-local Brin-Katok entropy. Besides, for subshifts of finite type, we prove that alpha-Bowen topological entropy is closely related to spectral radius and Hausdorff dimension.

Keywords:

alpha-BS dimension

Bowen's equation

alpha-local Brin-Katok entropy

Variational principle

α-BS dimension on subsets

Abstract

Journal

Organization