Thermodynamic formalism of GL2(R)-cocycles with canonical holonomies

Clark Butler, Kiho Park

Research output: Contribution to journalArticlepeer-review

Abstract

We study the norm potentials of Hölder continuous GL2(R)-cocycles over hyperbolic systems whose canonical holonomies converge and are Hölder continuous. Such cocycles include locally constant GL2(R)-cocycles as well as fiber-bunched GL2(R)-cocycles. We show that the norm potentials of irreducible such cocycles have unique equilibrium states. Among the reducible cocycles, we provide a characterization for cocycles whose norm potentials have more than one equilibrium states.

Original languageEnglish (US)
Pages (from-to)2141-2166
Number of pages26
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume41
Issue number5
DOIs
StatePublished - May 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Keywords

  • Equilibrium states
  • Gibbs property
  • Linear cocycles
  • Norm potentials
  • Subadditive thermodynamic formalism

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