Removal of Phase Transition in the Chebyshev Quadratic and Thermodynamics for Hénon-Like Maps Near the First Bifurcation

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Abstract

It is well-known that the geometric pressure function (formula presented.) of the Chebyshev quadratic map T2(x) = 1 - 2 x2(x∈ R) is not differentiable at t= - 1. We show that this phase transition can be “removed”, by an arbitrarily small singular perturbation of the map T2 into Hénon-like diffeomorphisms. A proof of this result relies on an elaboration of the well-known inducing techniques adapted to Hénon-like dynamics near the first bifurcation.

Original languageEnglish
Pages (from-to)1354-1378
Number of pages25
JournalJournal of Statistical Physics
Volume164
Issue number6
DOIs
Publication statusPublished - 2016 Sep 1

Keywords

  • Chebyshev quadratic map
  • Hénon-like maps
  • Phase transition
  • Thermodynamic formalism

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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