TY - JOUR

T1 - Equilibrium measures for the Hénon map at the first bifurcation

T2 - Uniqueness and geometric/statistical properties

AU - Senti, Samuel

AU - Takahasi, Hiroki

PY - 2014/9/16

Y1 - 2014/9/16

N2 - 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 non-continuous geometric potential , where is in a certain large interval and denotes the Jacobian in the unstable direction. We obtain geometric and statistical properties of these measures.

AB - 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 non-continuous geometric potential , where is in a certain large interval and denotes the Jacobian in the unstable direction. We obtain geometric and statistical properties of these measures.

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U2 - 10.1017/etds.2014.61

DO - 10.1017/etds.2014.61

M3 - Article

AN - SCOPUS:84951765841

VL - 36

SP - 215

EP - 255

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

IS - 1

ER -