Certain new robust properties of invariant sets and attractors of dynamical systems

DOI10.1007/BF02465190zbMath0939.37015OpenAlexW2000178348WikidataQ56029952 ScholiaQ56029952MaRDI QIDQ1966301

A. S. Gorodetskii, Yulij S. Ilyashenko

Publication date: 6 July 2000

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02465190

zbMATH Keywords

attractorsinvariant setdiffeomorphismsperiodic pointsLyapunov exponentdense orbits

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

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Cites Work

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• Dynamics: a probabilistic and geometric perspective
• Contributions to the stability conjecture
• Stable ergodicity of skew extensions by compact Lie groups
• Unstable dimension variability: A source of nonhyperbolicity in chaotic systems
• Stably ergodic diffeomorphisms
• Persistent nonhyperbolic transitive diffeomorphisms
• Cohomology of dynamical systems and rigidity of partially hyperbolic actions of higher-rank lattices
• SRB measures for partially hyperbolic systems whose central direction is mostly contracting
• An open set of maps for which every point is absolutely nonshadowable
• Invariant manifolds

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