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

Hiroki Takahasi

doi:10.1007/s10955-016-1584-y

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

Hiroki Takahasi

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	1-25
Number of pages	25
Journal	Journal of Statistical Physics
DOIs	https://doi.org/10.1007/s10955-016-1584-y
Publication status	Accepted/In press - 2016 Aug 10

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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N2 - 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.

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 - Thermodynamic formalism

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