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Uniqueness and stability of equilibrium states for random non-uniformly expanding maps

Part of: General theory of linear operators Dynamical systems with hyperbolic behavior

Published online by Cambridge University Press:  27 July 2022

R. BILBAO Open the ORCID record for R. BILBAO [Opens in a new window]  and
V. RAMOS
R. BILBAO
Affiliation:
Escuela de Matemática y Estatística, UPTC, Sede Central del Norte Av. Central del Norte 39-115, cod. 150003 Tunja, Boyacá, Colombia (e-mail: rafael.alvarez@uptc.edu.co)
V. RAMOS*
Affiliation:
Departamento de Matemática, UFMA, Av. dos Portugueses, 1966, 65080-805 São Luís, Maranhão, Brazil
*
e-mail: ramos.vanessa@ufma.br
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Abstract

We consider a robust class of random non-uniformly expanding local homeomorphisms and Hölder continuous potentials with small variation. For each element of this class we develop the thermodynamical formalism and prove the existence and uniqueness of equilibrium states among non-uniformly expanding measures. Moreover, we show that these equilibrium states and the random topological pressure vary continuously in this setting.

Keywords

random dynamical systemsstabilitythermodynamical formalism

MSC classification

Primary: 37D25: Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) 37D35: Thermodynamic formalism, variational principles, equilibrium states
Secondary: 47A15: Invariant subspaces 47A35: Ergodic theory
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 43 , Issue 8 , August 2023 , pp. 2589 - 2623
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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