Uniform (projective) hyperbolicity or no hyperbolicity: a dichotomy for generic conservative maps

DOI10.1016/S0294-1449(01)00094-4zbMath1125.37308OpenAlexW2050860224WikidataQ125366756 ScholiaQ125366756MaRDI QIDQ1611401

Jairo Bochi, Marcelo Viana

Publication date: 16 September 2002

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_2002__19_1_113_0

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Generic properties, structural stability of dynamical systems (37C20) Partially hyperbolic systems and dominated splittings (37D30)

Related Items (14)

Conditions for dominated splittings ⋮ Breaking hyperbolicity for smooth symplectic toral diffeomorphisms ⋮ AN OPEN SET OF UNBOUNDED COCYCLES WITH SIMPLE LYAPUNOV SPECTRUM AND NO EXPONENTIAL SEPARATION ⋮ Nonhyperbolic dynamics by mingling, blending, and flip-flopping ⋮ Parametric Furstenberg theorem on random products of \(\mathrm{SL}(2, \mathbb{R})\) matrices ⋮ Existence and genericity problems for dynamical systems with nonzero Lyapunov exponents ⋮ Persistence of nonhyperbolic measures for \(C^{1}\)-diffeomorphisms ⋮ Dominated splitting versus small angles ⋮ Entropy spectrum of Lyapunov exponents for nonhyperbolic step skew-products and elliptic cocycles ⋮ Non-hyperbolic ergodic measures for non-hyperbolic homoclinic classes ⋮ C¹-generic symplectic diffeomorphisms: partial hyperbolicity and zero centre Lyapunov exponents ⋮ Partial hyperbolicity or dense elliptic periodic points for 𝐶¹-generic symplectic diffeomorphisms ⋮ Nonremovable zero Lyapunov exponent ⋮ Uniform (projective) hyperbolicity or no hyperbolicity: a dichotomy for generic conservative maps

Cites Work

• Une méthode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2
• Analycity properties of the characteristic exponents of random matrix products
• Uniform (projective) hyperbolicity or no hyperbolicity: a dichotomy for generic conservative maps
• A formula with some applications to the theory of Lyapunov exponents
• Genericity of zero Lyapunov exponents
• Lyapunov exponents with multiplicity 1 for deterministic products of matrices
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
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