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 (Formula presented.)(Formula presented.) is not differentiable at (Formula presented.). We show that this phase transition can be “removed”, by an arbitrarily small singular perturbation of the map (Formula presented.) 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)1-25
Number of pages25
JournalJournal of Statistical Physics
DOIs
Publication statusAccepted/In press - 2016 Aug 10

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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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