Dimension Estimates for Non-conformal Repellers and Continuity of Sub-additive Topological Pressure

Yongluo Cao, Yakov Pesin, Yun Zhao

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

Given a non-conformal repeller Λ of a C1 + γ map, we study the Hausdorff dimension of the repeller and continuity of the sub-additive topological pressure for the sub-additive singular valued potentials. Such a potential always possesses an equilibrium state. We then use a substantially modified version of Katok’s approximating argument, to construct a compact invariant set on which the corresponding dynamical quantities (such as Lyapunov exponents and metric entropy) are close to that of the equilibrium measure. This allows us to establish continuity of the sub-additive topological pressure and obtain a sharp lower bound of the Hausdorff dimension of the repeller. The latter is given by the zero of the super-additive topological pressure.

Original languageEnglish (US)
Pages (from-to)1325-1368
Number of pages44
JournalGeometric and Functional Analysis
Volume29
Issue number5
DOIs
StatePublished - Oct 1 2019

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology

Fingerprint Dive into the research topics of 'Dimension Estimates for Non-conformal Repellers and Continuity of Sub-additive Topological Pressure'. Together they form a unique fingerprint.

  • Cite this