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

Clark Butler; Kiho Park

doi:10.3934/dcds.2020356

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

Clark Butler, Kiho Park

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 language	English (US)
Pages (from-to)	2141-2166
Number of pages	26
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	41
Issue number	5
DOIs	https://doi.org/10.3934/dcds.2020356
State	Published - May 2021

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

Access to Document

10.3934/dcds.2020356

Cite this

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abstract = "We study the norm potentials of H{\"o}lder continuous GL2(R)-cocycles over hyperbolic systems whose canonical holonomies converge and are H{\"o}lder 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.",

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AB - 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.

KW - Equilibrium states

KW - Gibbs property

KW - Linear cocycles

KW - Norm potentials

KW - Subadditive thermodynamic formalism

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