Phase Transitions for one-dimensional Lorenz-like expanding Maps

DOI10.1007/S00574-022-00310-YarXiv2005.03558MaRDI QIDQ6340246

Juliano G. Oler, Márcio R. Alves Gouveia

Publication date: 7 May 2020

Abstract: Given an one-dimensional Lorenz-like expanding map we prove that the conditionlinebreak $P_{top}(phi,partialmathcalP,ell)<P_{top}(phi,ell)$ (see, subsection 2.4 for definition), introduced by Buzzi and Sarig in [1] is satisfied for all continuous potentials $phi:[0,1]longrightarrowmathbbR$. We apply this to prove that quasi-H"older-continuous potentials (see, subsection 2.2 for definition) have at most one equilibrium measure and we construct a family of continuous but not H"older and neither weak H"older continuous potentials for which we observe phase transitions. Indeed, this class includes all H"older and weak-H"older continuous potentials and form an open and [2].

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Partially hyperbolic systems and dominated splittings (37D30) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

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