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 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 language	English
Pages (from-to)	1354-1378
Number of pages	25
Journal	Journal of Statistical Physics
Volume	164
Issue number	6
DOIs	https://doi.org/10.1007/s10955-016-1584-y
Publication status	Published - 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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10.1007/s10955-016-1584-y

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title = "Removal of Phase Transition in the Chebyshev Quadratic and Thermodynamics for H{\'e}non-Like Maps Near the First Bifurcation",

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 H{\'e}non-like diffeomorphisms. A proof of this result relies on an elaboration of the well-known inducing techniques adapted to H{\'e}non-like dynamics near the first bifurcation.",

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N2 - 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.

AB - 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.

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KW - Hénon-like maps

KW - Phase transition

KW - Thermodynamic formalism

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

Abstract

Keywords

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