Equilibrium measures for the Hénon map at the first bifurcation

Samuel Senti; Hiroki Takahasi

doi:10.1088/0951-7715/26/6/1719

Equilibrium measures for the Hénon map at the first bifurcation

Samuel Senti, Hiroki Takahasi

Department of Mathematics

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

12 Citations (Scopus)

Abstract

We study the dynamics of strongly dissipative Hénon maps at the first bifurcation parameter where the uniform hyperbolicity is destroyed by the formation of tangencies inside the limit set. We prove the existence of an equilibrium measure which minimizes the free energy associated with the non-continuous potential -t logJ^u, where is in a certain interval of the form (-∞, t₀), t₀ > 0 and J^u denotes the Jacobian in the unstable direction.

Original language	English
Pages (from-to)	1719-1741
Number of pages	23
Journal	Nonlinearity
Volume	26
Issue number	6
DOIs	https://doi.org/10.1088/0951-7715/26/6/1719
Publication status	Published - 2013 Jun

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)
Applied Mathematics

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10.1088/0951-7715/26/6/1719

Cite this

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abstract = "We study the dynamics of strongly dissipative H{\'e}non maps at the first bifurcation parameter where the uniform hyperbolicity is destroyed by the formation of tangencies inside the limit set. We prove the existence of an equilibrium measure which minimizes the free energy associated with the non-continuous potential -t logJu, where is in a certain interval of the form (-∞, t0), t0 > 0 and Ju denotes the Jacobian in the unstable direction.",

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AB - We study the dynamics of strongly dissipative Hénon maps at the first bifurcation parameter where the uniform hyperbolicity is destroyed by the formation of tangencies inside the limit set. We prove the existence of an equilibrium measure which minimizes the free energy associated with the non-continuous potential -t logJu, where is in a certain interval of the form (-∞, t0), t0 > 0 and Ju denotes the Jacobian in the unstable direction.

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Equilibrium measures for the Hénon map at the first bifurcation

Abstract

ASJC Scopus subject areas

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