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Research demonstrates unique equilibrium states and large deviation principles in the Katok map, indicating significant properties of non-uniformly hyperbolic systems.
We study the thermodynamic formalism of a C∞ non-uniformly hyperbolic diffeomorphism on the 2-torus, known as the Katok map. We prove for a Hölder continuous potential with one additional condition, or the geometric t-potential φₜ with $t<1$, the equilibrium state exists and is unique. We derive the level-2 large deviation principle for the equilibrium state of φₜ. We study the multifractal spectra of the Katok map for the entropy and dimension of level sets of Lyapunov exponents.
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Tianyu Wang (2019) studied this question.
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