Invariance entropy of hyperbolic control sets

DOI10.3934/dcds.2016.36.97zbMath1317.93133arXiv1408.2416OpenAlexW2963336978MaRDI QIDQ2515672

Adriano Da Silva, Christoph Kawan

Publication date: 6 August 2015

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.2416

zbMATH Keywords

hyperbolicityshadowing lemmachain control setsinvariance entropycontrol setscontrol-affine systemsuniversally regular controlsvolume lemma

Mathematics Subject Classification ID

Controllability (93B05) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Control/observation systems governed by ordinary differential equations (93C15) Nonautonomous smooth dynamical systems (37C60)

Related Items (21)

Invariance entropy for a class of partially hyperbolic sets ⋮ Control Sets for Affine Systems, Spectral Properties, and Projective Spaces ⋮ Hyperbolic chain control sets on flag manifolds ⋮ Invariance entropy, quasi-stationary measures and control sets ⋮ Equi-invariability and bounded invariance complexity for control systems ⋮ Measure-Theoretic Invariance Entropy for Control Systems ⋮ Mini-workshop: Entropy, information and control. Abstracts from the mini-workshop held March 4--10, 2018 ⋮ Observation of nonlinear systems via finite capacity channels. II: Restoration entropy and its estimates ⋮ Invariance pressure for control systems ⋮ Equi-invariability, bounded invariance complexity and L-stability for control systems ⋮ Metric invariance entropy and conditionally invariant measures ⋮ Controllability near a homoclinic bifurcation ⋮ Control systems on flag manifolds and their chain control sets ⋮ Robustness of critical bit rates for practical stabilization of networked control systems ⋮ Bounds for invariance pressure ⋮ Stationary and Ergodic Properties of Stochastic NonLinear Systems Controlled over Communication Channels ⋮ Lyapunov exponents and partial hyperbolicity of chain control sets on flag manifolds ⋮ Entropy for Practical Stabilization ⋮ Outer invariance entropy for discrete-time linear systems on Lie groups ⋮ On the structure of uniformly hyperbolic chain control sets ⋮ Controllability properties and invariance pressure for linear discrete-time systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Growth rates for semiflows on Hausdorff spaces
• Volume growth and entropy
• Random perturbations of Axiom A basic sets
• Hyperbolic control sets and chain control sets
• Invariance entropy for deterministic control systems. An introduction
• Invariance Entropy of Control Sets
• Invariance Entropy for Control Systems
• Morse and Lyapunov spectra and dynamics on flag bundles
• Finite-dimensional open-loop control generators for non-linear systems
• An integral formula for topological entropy of $C^{\infty}$ maps
• Simplicial dynamical systems
• Linearized Control Systems and Applications to Smooth Stabilization
• Ergodic theory for axiom A endomorphisms
• Topological Feedback Entropy and Nonlinear Stabilization
• Escape rates and conditionally invariant measures
• Periodic Orbits for Hyperbolic Flows
• Some Large Deviation Results for Dynamical Systems
• The dynamics of control. With an appendix by Lars Grüne

This page was built for publication: Invariance entropy of hyperbolic control sets