Thermodynamic formalism for a family of non-uniformly hyperbolic horseshoes and the unstable Jacobian

DOI10.1017/S0143385709001126zbMath1225.37040MaRDI QIDQ3002596

Renaud Leplaideur

Publication date: 20 May 2011

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

Lyapunov exponentsthermodynamic formalismequilibrium stateshomoclinic tangenciesnon-uniformly hyperbolic horseshoes

Mathematics Subject Classification ID

Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items (4)

Removal of phase transition in the Chebyshev quadratic and thermodynamics for Hénon-like maps near the first bifurcation ⋮ Equilibrium Measures at Temperature Zero for Hénon-Like Maps at the First Bifurcation ⋮ Boundary of the Horseshoe Locus for the Hénon Family ⋮ Equilibrium measures for the Hénon map at the first bifurcation: uniqueness and geometric/statistical properties

Cites Work

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• Equilibrium states for S-unimodal maps
• Gibbs measures at temperature zero
• ON THERMODYNAMICS OF RATIONAL MAPS. II: NON-RECURRENT MAPS
• Local product structure for Equilibrium States
• A dynamical proof for the convergence of Gibbs measures at temperature zero

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