Robust transitivity of singular hyperbolic attractors

DOI10.1007/s00209-020-02618-1zbMath1476.37044arXiv2001.07293OpenAlexW3087556412WikidataQ115609047 ScholiaQ115609047MaRDI QIDQ2031720

Sylvain Crovisier, Da-Wei Yang

Publication date: 10 June 2021

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.07293

zbMATH Keywords

uniform hyperbolicitysingular hyperbolicityrobust topological properties

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Generic properties, structural stability of dynamical systems (37C20) Dynamical systems with hyperbolic orbits and sets (37D05) Partially hyperbolic systems and dominated splittings (37D30) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

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Cites Work

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• Homoclinic classes for sectional-hyperbolic sets
• On the singular-hyperbolicity of star flows
• Indices of singularities of robustly transitive sets
• Structural stability of Lorenz attractors
• Sufficient conditions for robustness of attractors
• Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers
• On the notions of singular domination and (multi-)singular hyperbolicity
• On the density of singular hyperbolic three-dimensional vector fields: a conjecture of Palis
• Mixing properties and statistical limit theorems for singular hyperbolic flows without a smooth stable foliation
• Dynamical properties of singular-hyperbolic attractors
• Stability of mixing and rapid mixing for hyperbolic flows
• Dominated chain recurrent class with singularities
• Recent progress on sectional-hyperbolic systems
• Three-Dimensional Flows
• Sectional-hyperbolic systems
• Singular-hyperbolic attractors are chaotic
• Robust transitivity and topological mixing for 𝐶¹-flows
• A dichotomy for three-dimensional vector fields
• Deterministic Nonperiodic Flow
• Morse-Smale systems and horseshoes for three dimensional singular flows
• Hyperbolic Limit Sets
• Recurrence and genericity