Lyapunov exponents, periodic orbits, and horseshoes for semiflows on Hilbert spaces

DOI10.1090/S0894-0347-2012-00734-6zbMath1263.37080MaRDI QIDQ2892813

Zeng Lian, Lai-Sang Young

Publication date: 25 June 2012

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Lyapunov exponentsergodic theorysemi-flowshorseshoesinfinite dimensional dynamical systems

Mathematics Subject Classification ID

Infinite-dimensional dissipative dynamical systems (37Lxx) Dynamical systems with hyperbolic behavior (37Dxx)

Related Items (26)

The approximation of uniform hyperbolicity for \(C^1\) diffeomorphisms with hyperbolic measures ⋮ The existence of semi-horseshoes for partially hyperbolic diffeomorphisms ⋮ Understanding Chaotic Dynamical Systems ⋮ Subadditive and multiplicative ergodic theorems ⋮ A shadowing lemma for quasi-hyperbolic strings of flows ⋮ A criterion for the triviality of the centralizer for vector fields and applications ⋮ Generalized Lyapunov exponents and aspects of the theory of deep learning ⋮ Horseshoes and Lyapunov exponents for Banach cocycles over non-uniformly hyperbolic systems ⋮ Observing Lyapunov exponents of infinite-dimensional dynamical systems ⋮ Lyapunov exponents, periodic orbits and horseshoes for mappings of Hilbert spaces ⋮ Fine properties of \(L^p\)-cocycles which allow abundance of simple and trivial spectrum ⋮ Periodic approximation of Lyapunov exponents for Banach cocycles ⋮ On the growth rate of periodic orbits for vector fields ⋮ Estimation of topological entropy in random dynamical systems ⋮ Entropy, volume growth and SRB measures for Banach space mappings ⋮ Generalizations of SRB measures to nonautonomous, random, and infinite dimensional systems ⋮ The Lyapunov exponents of generic skew-product compact semiflows ⋮ Existence of periodic orbits and horseshoes for mappings in a separable Banach space ⋮ Entropy of partially hyperbolic flows with center dimension two ⋮ The weak Smale horseshoe and mean hyperbolicity ⋮ Horseshoes for Anosov systems on fibers driven by an equicontinuous system ⋮ Existence of periodic orbits and horseshoes for semiflows on a separable Banach space ⋮ The existence of semi-horseshoes for \(C^1\) partially hyperbolic attractors in a Banach space ⋮ Livšic theorem for matrix cocycles over an axiom a flow ⋮ Continuity of sub-additive topological pressure with matrix cocycles ^* ⋮ Shy shadows of infinite-dimensional partially hyperbolic invariant sets

Cites Work

• Lyapunov exponents, periodic orbits and horseshoes for mappings of Hilbert spaces
• The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
• Fibres dynamiques asymptotiquement compacts, exposants de Lyapunov. Entropie. Dimension. (Asymptotically compact dynamical bundles, Lyapunov exponents. Entropy. Dimension)
• Ergodic theory of differentiable dynamical systems
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• Geometric theory of semilinear parabolic equations
• Characteristic exponents and invariant manifolds in Hilbert space
• Infinite-dimensional dynamical systems in mechanics and physics.
• Lyapunov exponents and invariant manifolds for random dynamical systems in a Banach space
• An inequality for the entropy of differentiable maps
• CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
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