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

Samuel Senti, Hiroki Takahasi

Research output: Contribution to journalArticle

1 Citation (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
JournalErgodic Theory and Dynamical Systems
Volume760
DOIs
Publication statusPublished - 2014 Nov 17

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Equilibrium Measure
Statistical property
Free energy
Uniqueness
Bifurcation
Thermodynamics
Thermodynamic Formalism
Limit Set
Hyperbolicity
Invariant Measure
Probability Measure
Free Energy
Existence and Uniqueness
Unstable
Denote
Minimise
Interval

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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