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Equilibrium measures for two-sided shift spaces via dimension theory
Part of:
Dynamical systems with hyperbolic behavior
Topological dynamics
Smooth dynamical systems: general theory
Published online by Cambridge University Press: 10 September 2024
Abstract
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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- Original Article
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- © The Author(s), 2024. Published by Cambridge University Press
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