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

The first author is supported by Oswald Veblen fund

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  • 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.


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