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.
ASJC Scopus subject areas
- Applied Mathematics