STOCHASTIC STABILITY OF NON-UNIFORMLY HYPERBOLIC DIFFEOMORPHISMS

DOI10.1142/S0219493707002049zbMath1210.37022OpenAlexW1993022490MaRDI QIDQ3502797

Carlos H. Vásquez, José F. Alves, Vítor Araújo

Publication date: 20 May 2008

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219493707002049

zbMATH Keywords

stochastic stabilityrandom perturbationSRB measuredominated splittingnon-uniform hyperbolicity

Mathematics Subject Classification ID

Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items

A classification of the dynamics of three-dimensional stochastic ecological systems ⋮ Adapted random perturbations for non-uniformly expanding maps ⋮ SRB measures for partially hyperbolic systems whose central direction is weakly expanding ⋮ Stochastic stability for partially hyperbolic diffeomorphisms with mostly expanding and mostly contracting centers ⋮ Physical measures and absolute continuity for one-dimensional center direction ⋮ Empiric Stochastic Stability of Physical and Pseudo-physical Measures ⋮ Strong stochastic stability for non-uniformly expanding maps ⋮ Uniform hyperbolicity on random sets ⋮ Approximating invariant densities of metastable systems ⋮ Almost sure rates of mixing for partially hyperbolic attractors

Cites Work

• Random perturbations and statistical properties of Hénon-like maps
• The ergodic theory of axiom A flows
• Contributions to the stability conjecture
• What are SRB measures, and which dynamical systems have them?
• SRB measures for partially hyperbolic systems whose central direction is mostly expanding
• Attractors and time averages for random maps
• On dynamics of mostly contracting diffeomorphisms
• Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers
• Smooth ergodic theory of random dynamical systems
• SRB measures for partially hyperbolic systems whose central direction is mostly contracting
• Infinitely many stochastically stable attractors
• Statistical stability for diffeomorphisms with dominated splitting
• A Measure Associated with Axiom-A Attractors
• FAMILIES OF INVARIANT MANIFOLDS CORRESPONDING TO NONZERO CHARACTERISTIC EXPONENTS
• Singular hyperbolic systems
• The Lorenz attractor exists