Entropy and the Hausdorff dimension for infinite-dimensional dynamical systems

DOI10.1007/BF01048158zbMath0744.34047MaRDI QIDQ1183225

Philippe Thieullen

Publication date: 28 June 1992

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

zbMATH Keywords

Banach spacesHausdorff dimension of global attractorssequence of uniform Lyapunov exponents

Mathematics Subject Classification ID

Related Items (14)

On stability of discrete dynamical systems: from global methods to ergodic theory approaches ⋮ Lower bounds for the Hausdorff dimension of attractors ⋮ On some properties of the shift on an infinite-dimensional torus ⋮ Unnamed Item ⋮ Entropies of commuting transformations on Hilbert spaces ⋮ Attractors for Nonautonomous Navier–Stokes System and Other Partial Differential Equations ⋮ Maximum local Lyapunov dimension bounds the box dimension. Direct proof for invariant sets on Riemannian manifolds ⋮ On the finite dimension of attractors of parabolic problems in \(\mathbb R^N\) with general potentials ⋮ The metric entropy of random dynamical systems in a Banach space: Ruelle inequality ⋮ A version of the theorem of Johnson, Palmer, and Sell for quasicompact cocycles ⋮ On the asymptotic behavior of discrete dynamical systems -- an ergodic theory approach ⋮ Explicit bounds for separation between Oseledets subspaces ⋮ On a class of Anosov diffeomorphisms on the infinite-dimensional torus ⋮ Dimension spectra and a mathematical model for phase transition

Cites Work

• Regular attractors of semigroups and evolution equations
• Fibres dynamiques asymptotiquement compacts, exposants de Lyapunov. Entropie. Dimension. (Asymptotically compact dynamical bundles, Lyapunov exponents. Entropy. Dimension)
• Ergodic theory of differentiable dynamical systems
• Entropy numbers, s-numbers, and eigenvalue problems
• Some relations between dimension and Lyapunov exponents
• Characteristic exponents and invariant manifolds in Hilbert space
• The subadditive ergodic theorem and recurrence properties of Markovian transformations
• Attractors representing turbulent flows
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Entropy and the Hausdorff dimension for infinite-dimensional dynamical systems