Equilibrium measures at temperature zero for Hénon-like maps at the first bifurcation

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6 Citations (Scopus)

Abstract

We develop a thermodynamic formalism for a strongly dissipative Hénon-like map at the first bifurcation parameter at which the uniform hyperbolicity is destroyed by the formation of tangencies inside the limit set. For any t ∈ ℝ we prove the existence of an invariant Borel probability measure which minimizes the free energy associated with a noncontinuous geometric potential -t log Ju, where Ju denotes the Jacobian in the unstable direction. We characterize accumulation points of these measures as t→±∞ in terms of the unstable Lyapunov exponent.

Original languageEnglish
Pages (from-to)106-124
Number of pages19
JournalSIAM Journal on Applied Dynamical Systems
Volume15
Issue number1
DOIs
Publication statusPublished - 2016

Keywords

  • First bifurcation
  • Hénon-like maps
  • Thermodynamic formalism

ASJC Scopus subject areas

  • Analysis
  • Modelling and Simulation

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