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

Samuel Senti, Hiroki Takahasi

9 被引用数 (Scopus)

## 抄録

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.

本文言語 English 215-255 41 Ergodic Theory and Dynamical Systems 760 https://doi.org/10.1017/etds.2014.61 Published - 2014 11月 17

• 数学 (全般)
• 応用数学

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