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

研究成果: Article

抄録

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.

元の言語English
ページ(範囲)1-25
ページ数25
ジャーナルJournal of Statistical Physics
DOI
出版物ステータスAccepted/In press - 2016 8 10

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Chebyshev
Thermodynamics
Phase Transition
Bifurcation
thermodynamics
Quadratic Map
Singular Perturbation
Diffeomorphisms
Small Perturbations
Differentiable
perturbation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

これを引用

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AB - 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.

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KW - Phase transition

KW - Thermodynamic formalism

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