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Award ID contains: 2154378

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  1. ; (, Ergodic Theory and Dynamical Systems)
    Given a two-sided shift space on a finite alphabet and a continuous potential function, we give conditions under which an equilibrium measure can be described using a construction analogous to Hausdorff measure that goes back to the work of Bowen. This construction was previously applied to smooth uniformly and partially hyperbolic systems by the first author, Pesin, and Zelerowicz. Our results here apply to all subshifts of finite type and Hölder continuous potentials, but extend beyond this setting, and we also apply them to shift spaces with synchronizing words. 
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    Free, publicly-accessible full text available February 1, 2026
  2. (, Discrete and Continuous Dynamical Systems)
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  3. ; ; ; (, Communications in Mathematical Physics)
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  4. (, Ergodic Theory and Dynamical Systems)
    We study equilibrium states for a class of non-uniformly expanding skew products, and show how a family of fiberwise transfer operators can be used to define the conditional measures along fibers of the product. We prove that the pushforward of the equilibrium state onto the base of the product is itself an equilibrium state for a Hölder potential defined via these fiberwise transfer operators. 
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