Newhouse phenomenon and homoclinic classes

DOI10.1017/S0143385710000465zbMath1276.37032arXiv0712.0513MaRDI QIDQ3093797

Jiagang Yang

Publication date: 18 October 2011

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.0513

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Cites Work

• Connecting invariant manifolds and the solution of the \(C^ 1\) stability and \(\Omega\)-stability conjectures for flows
• Density of hyperbolicity and tangencies in sectional dissipative regions
• Periodic orbits and chain-transitive sets of \(C^1\)-diffeomorphisms
• The selecting lemma of Liao
• Minimal non-hyperbolicity and index-completeness
• A proof of the \(C^ 1\) stability conjecture
• Another proof for \(C^1\) stability conjecture for flows
• High dimension diffeomorphisms displaying infinitely many periodic attractors
• A \(C^1\)-generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks of sources
• Heteroclinic cycles and homoclinic closures for generic diffeomorphisms
• The star systems \({\mathcal H}^*\) and a proof of the \(C^1 \Omega\)-stability conjecture for flows
• Homoclinic tangencies and hyperbolicity for surface diffeomorphisms
• An ergodic closing lemma
• Persistent nonhyperbolic transitive diffeomorphisms
• On the \(C^ 1\) stability conjecture for flows
• SRB measures for partially hyperbolic systems whose central direction is mostly contracting
• Diffeomorphisms with infinitely many sinks
• Nonsingular star flows satisfy Axiom A and the no-cycle condition
• Generic diffeomorphisms away from homoclinic tangencies and heterodimensional cycles
• Perturbations of the derivative along periodic orbits
• 𝐶¹ Connecting Lemmas
• Homoclinic tangencies and dominated splittings
• Robust nonhyperbolic dynamics and heterodimensional cycles
• Persistence of homoclinic tangencies in higher dimensions
• Persistence of cycles and nonhyperbolic dynamics at heteroclinic bifurcations
• Global dominated splittings and the $C^1$ Newhouse phenomenon
• On the existence of non-trivial homoclinic classes
• Adapted metrics for dominated splittings
• Differentiable dynamical systems
• Recurrence and genericity

This page was built for publication: Newhouse phenomenon and homoclinic classes