Title
"Equilibrium measures for the H'enon map at the first bifurcation"
Hiroki Takahasi (Keio University)
Abstract
For strongly dissipative H'enon 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., prove the existence and uniqueness of an invariant probability measure which minimizes the free energy associated with a non continuous geometric potential $-tlog J^u$, where $tinmathbb R$ is in a certain large interval and $J^u$ denotes the Jacobian in the unstable direction. We obtain geometric and statistical properties of these measures.
