Equilibrium measures for the Hénon map at the first bifurcation

Samuel Senti, Hiroki Takahasi

Research output: Contribution to journalArticlepeer-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 logJu, where is in a certain interval of the form (-∞, t0), t0 > 0 and Ju denotes the Jacobian in the unstable direction.

Original languageEnglish
Pages (from-to)1719-1741
Number of pages23
JournalNonlinearity
Volume26
Issue number6
DOIs
Publication statusPublished - 2013 Jun 1

ASJC Scopus subject areas

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

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