### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 215-255 |

Number of pages | 41 |

Journal | Ergodic Theory and Dynamical Systems |

Volume | 36 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2014 Sep 16 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Equilibrium measures for the Hénon map at the first bifurcation : Uniqueness and geometric/statistical properties.** / Senti, Samuel; Takahasi, Hiroki.

Research output: Contribution to journal › Article

*Ergodic Theory and Dynamical Systems*, vol. 36, no. 1, pp. 215-255. https://doi.org/10.1017/etds.2014.61

}

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.

UR - http://www.scopus.com/inward/record.url?scp=84951765841&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84951765841&partnerID=8YFLogxK

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 -