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Equilibrium states for non-uniformly expanding skew products

Part of: Smooth dynamical systems: general theory Dynamical systems with hyperbolic behavior

Published online by Cambridge University Press:  11 December 2023

GREGORY HEMENWAY
GREGORY HEMENWAY*
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, OH 43232, USA
*
e-mail: hemenway.math@gmail.com
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Abstract

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.

Keywords

equilibrium statesRPF transfer operatornon-uniformly expandingskew products

MSC classification

Primary: 37D35: Thermodynamic formalism, variational principles, equilibrium states
Secondary: 37C30: Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , First View , pp. 1 - 22
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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