Equilibrium measures for the Hénon map at the first bifurcation: Uniqueness and geometric/statistical properties

Samuel Senti, Hiroki Takahasi

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

For 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 establish a thermodynamic formalism, i.e. we prove the existence and uniqueness of an invariant probability measure that minimizes the free energy associated with a noncontinuous geometric potential -t log Ju, where t 2 R is in a certain large interval and Ju denotes the Jacobian in the unstable direction. We obtain geometric and statistical properties of these measures.

Original languageEnglish
Pages (from-to)215-255
Number of pages41
JournalErgodic Theory and Dynamical Systems
Volume760
DOIs
Publication statusPublished - 2014 Nov 17

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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