TY - JOUR

T1 - Thermodynamic Formalism for Random Non-uniformly Expanding Maps

AU - Stadlbauer, Manuel

AU - Suzuki, Shintaro

AU - Varandas, Paulo

N1 - Funding Information:
MS was partially supported by CNPq—Brazil, through grants PQ 312632/2018-5 and Universal 426814/2016-9, SS was partially supported by a PNPD-CAPES Postdoctoral fellowship at UFBA, and PV was partially supported by CNPq—Brazil and by Fundação para a Ciência e Tecnologia (FCT)—Portugal, through the grant CEECIND/03721/2017 of the Stimulus of Scientific Employment, Individual Support 2017 Call. We are indebted to the three anonymous referees for the careful reading of the manuscript and number of suggestions that helped to improve the manuscript.
Funding Information:
MS was partially supported by CNPq?Brazil, through grants PQ 312632/2018-5 and Universal 426814/2016-9, SS was partially supported by a PNPD-CAPES Postdoctoral fellowship at UFBA, and PV was partially supported by CNPq?Brazil and by Funda??o para a Ci?ncia e Tecnologia (FCT)?Portugal, through the grant CEECIND/03721/2017 of the Stimulus of Scientific Employment, Individual Support 2017 Call. We are indebted to the three anonymous referees for the careful reading of the manuscript and number of suggestions that helped to improve the manuscript.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2021/7

Y1 - 2021/7

N2 - We develop a quenched thermodynamic formalism for a wide class of random maps with non-uniform expansion, where no Markov structure, no uniformly bounded degree or the existence of some expanding dynamics is required. We prove that every measurable and fibered C1-potential at high temperature admits a unique equilibrium state which satisfies a weak Gibbs property, and has exponential decay of correlations. The arguments combine a functional analytic approach for the decay of correlations (using Birkhoff cone methods) and Carathéodory-type structures to describe the relative pressure of not necessary compact invariant sets in random dynamical systems. We establish also a variational principle for the relative pressure of random dynamical systems.

AB - We develop a quenched thermodynamic formalism for a wide class of random maps with non-uniform expansion, where no Markov structure, no uniformly bounded degree or the existence of some expanding dynamics is required. We prove that every measurable and fibered C1-potential at high temperature admits a unique equilibrium state which satisfies a weak Gibbs property, and has exponential decay of correlations. The arguments combine a functional analytic approach for the decay of correlations (using Birkhoff cone methods) and Carathéodory-type structures to describe the relative pressure of not necessary compact invariant sets in random dynamical systems. We establish also a variational principle for the relative pressure of random dynamical systems.

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U2 - 10.1007/s00220-021-04088-w

DO - 10.1007/s00220-021-04088-w

M3 - Article

AN - SCOPUS:85111404647

VL - 385

SP - 369

EP - 427

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -