Article Contents
Article Contents

# Thermodynamic formalism of $\text{GL}_2(\mathbb{R})$-cocycles with canonical holonomies

The first author is supported by Oswald Veblen fund

• We study the norm potentials of Hölder continuous $\text{GL}_2(\mathbb{R})$-cocycles over hyperbolic systems whose canonical holonomies converge and are Hölder continuous. Such cocycles include locally constant $\text{GL}_2(\mathbb{R})$-cocycles as well as fiber-bunched $\text{GL}_2(\mathbb{R})$-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.

Mathematics Subject Classification: 37D35, 37C40, 37H15.

 Citation:

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