On the notions of singular domination and (multi-)singular hyperbolicity

DOI10.1007/s11425-019-1764-xzbMath1451.37041arXiv2003.07099OpenAlexW3081166486MaRDI QIDQ2198336

Jinhua Zhang, Sylvain Crovisier, Adriana da Luz, Da-Wei Yang

Publication date: 10 September 2020

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.07099

zbMATH Keywords

linear Poincaré flowmulti-singular hyperbolicitysingular dominationstar vector field

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Dynamical systems with hyperbolic orbits and sets (37D05) Partially hyperbolic systems and dominated splittings (37D30) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items (3)

An entropy dichotomy for singular star flows ⋮ Robust transitivity of singular hyperbolic attractors ⋮ The dynamics of vector fields with singularities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the singular-hyperbolicity of star flows
• Certain ergodic properties of a differential system on a compact differentiable manifold
• Indices of singularities of robustly transitive sets
• A proof of the \(C^ 1\) stability conjecture
• Structural stability of Lorenz attractors
• A uniform \(C^1\) connecting lemma.
• A \(C^1\)-generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks of sources
• Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers
• Correction to: Connecting invariant manifolds and the solution of the \(C^1\) stability and \(\Omega\)-stability conjectures for flows.
• An ergodic closing lemma
• Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective
• SRB measures for partially hyperbolic systems whose central direction is mostly contracting
• Robustly transitive singular sets via approach of an extended linear Poincaré flow
• Dominated splittings for flows with singularities
• Dominated chain recurrent class with singularities
• Perturbations of the derivative along periodic orbits
• Recent progress on sectional-hyperbolic systems
• Three-Dimensional Flows
• Sectional-hyperbolic systems
• 𝐶¹ Connecting Lemmas
• Deterministic Nonperiodic Flow
• Morse-Smale systems and horseshoes for three dimensional singular flows
• Differentiable dynamical systems

This page was built for publication: On the notions of singular domination and (multi-)singular hyperbolicity