The boundary of hyperbolicity for Hénon-like families

DOI10.1017/S0143385707000776zbMath1151.37036arXivmath/0502235MaRDI QIDQ3528750

Stefano Luzzatto, Isabel Rios, Yong-Luo Cao

Publication date: 17 October 2008

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

Full work available at URL: https://arxiv.org/abs/math/0502235

zbMATH Keywords

Hénon maphyperbolicityHénon-like familiesboundary of hyperbolicity

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (16)

Dynamical quantities and their numerical analysis by saddle periodic orbits ⋮ Birkhoff spectrum for Hénon-like maps at the first bifurcation ⋮ Removal of phase transition in the Chebyshev quadratic and thermodynamics for Hénon-like maps near the first bifurcation ⋮ Building thermodynamics for non-uniformly hyperbolic maps ⋮ On parameter loci of the Hénon family ⋮ Hyperbolic invariant sets of the real generalized Hénon maps ⋮ Horseshoes and Lyapunov exponents for Banach cocycles over non-uniformly hyperbolic systems ⋮ Prevalent dynamics at the first bifurcation of Hénon-like families ⋮ A symbolic characterization of the horseshoe locus in the Hénon family ⋮ Characterization of Dynamics of a Class of Polynomial Automorphisms in ℂn ⋮ Lyapunov spectrum for Hénon-like maps at the first bifurcation ⋮ Equilibrium Measures at Temperature Zero for Hénon-Like Maps at the First Bifurcation ⋮ Equilibrium measures for the Hénon map at the first bifurcation: uniqueness and geometric/statistical properties ⋮ Destroying horseshoes via heterodimensional cycles: generating bifurcations inside homoclinic classes ⋮ Thermodynamics of towers of hyperbolic type ⋮ Non-hyperbolic ergodic measures for non-hyperbolic homoclinic classes

Cites Work

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• CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
• FAMILIES OF INVARIANT MANIFOLDS CORRESPONDING TO NONZERO CHARACTERISTIC EXPONENTS
• Polynomial diffeomorphisms of C 2. VIII: quasi-expansion
• Parameter exclusions in Hénon-like systems
• Solution of the basin problem for Hénon-like attractors
• Strange attractors with one direction of instability

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