On the topological pressure of the saturated set with non-uniform structure

2016/05/25 by Cao Zhao, Zhao, Cao, Ercai Chen +1 · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1605.07845

openalex publication_date 2016/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive a conditional variational principle of the saturated set for systems with the non-uniform structure. Our result applies to a broad class of systems including beta-shifts, S-gap shifts and their factors.

Citations

• Variational principles and mixed multifractal spectra
• Sets of “Non-typical” points have full topological entropy and full Hausdorff dimension
• Irregular sets, the 𝛽-transformation and the almost specification property
• Invariant measures of full dimension for some expanding maps

Cited by

• Complete realization of multifractal entropy spectra and pressure functions

Related

• Variational relations of topological pressure for nonautonomous dynamical systems
• Variational principles for topological pressures on subsets
• A variational principle for topological pressure for certain non-compact sets
• The Asymptotically Additive Topological Pressure: Variational Principle For Non Compact and Intersection of Irregular Sets
• Variational principles of topological pressure for correspondences