Transfer operator and conformal measures for a class of maps having covering property

2013/03/28 by Jianhua Zheng, Jian-Hua Zheng, Zheng, Jian-Hua
Mathematics · #28D20 #37D35 #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Dynamics and Fractals #math.DS #msc:28D20 #msc:37D35

paper · pdf · doi:10.48550/arxiv.1303.7072

27 pages

arxiv created 2013/03/28 · openalex publication_date 2013/03/28 · arxiv updated 2013/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (X,d) be a metric space and X₀ be an open and dense subset of X. We develop the Walters' theory and discuss the existence of conformal measures in terms of the Perron-Frobenius-Ruelle operator for a continuous map T:X₀→ X and the Bowen formula about Hausdorff dimension and Poincaré exponent of some invariant subsests for T with some expanding property.

Related

• Invariant measures of full dimension for some expanding maps
• On the conformal gauge of a compact metric space
• Conformally Natural extensions revisited
• The boundary correspondence under quasiconformal mappings and VMO-Teichmuller space
• Pseudorandom Numbers for Conformal Measure