A robustly chain transitive attractor with singularities of different indices

DOI10.1017/S1474748012000710zbMath1304.37002MaRDI QIDQ2841758

Ming Li, Da-Wei Yang, Christian Bonatti

Publication date: 30 July 2013

Published in: Journal of the Institute of Mathematics of Jussieu (Search for Journal in Brave)

zbMATH Keywords

indexpartially hyperbolicsingular attractorrobustly chain transitive

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Partially hyperbolic systems and dominated splittings (37D30) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

Related Items (6)

Weak hyperbolic structures and robust properties of diffeomorphisms and flows ⋮ Robustly chain transitive sets with orbital shadowing diffeomorphisms ⋮ On the existence of attractors ⋮ Singular robustly chain transitive sets are singular volume partial hyperbolic ⋮ Star flows and multisingular hyperbolicity ⋮ Periodic shadowing of vector fields

Cites Work

• Connecting invariant manifolds and the solution of the \(C^ 1\) stability and \(\Omega\)-stability conjectures for flows
• Structural stability of Lorenz attractors
• Homoclinic bifurcations and uniform hyperbolicity for three-dimensional flows.
• Robustly transitive flows on compact manifolds
• A \(C^1\)-generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks of sources
• Homoclinic tangencies and hyperbolicity for surface diffeomorphisms
• Partial hyperbolicity and robust transitivity
• Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers
• An ergodic closing lemma
• Persistent nonhyperbolic transitive diffeomorphisms
• On the \(C^ 1\) stability conjecture for flows
• Nonsingular star flows satisfy Axiom A and the no-cycle condition
• Robustly transitive singular sets via approach of an extended linear Poincaré flow
• Generic diffeomorphisms away from homoclinic tangencies and heterodimensional cycles
• Perturbations of the derivative along periodic orbits
• On C1 robust singular transitive sets for three-dimensional flows
• Singular strange attractors on the boundary of Morse-Smale systems
• Attracteurs de Lorenz de variété instable de dimension arbitraire
• A dichotomy for three-dimensional vector fields
• Deterministic Nonperiodic Flow
• Homoclinic tangencies and dominated splittings
• The set of axiom A diffeomorphisms with no cycles
• The Closing Lemma

This page was built for publication: A robustly chain transitive attractor with singularities of different indices