CENTER MANIFOLDS FOR PARTIALLY HYPERBOLIC SETS WITHOUT STRONG UNSTABLE CONNECTIONS

DOI10.1017/S1474748015000055zbMath1362.37069arXiv1401.2452MaRDI QIDQ2976261

Sylvain Crovisier, Christian Bonatti

Publication date: 28 April 2017

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

Full work available at URL: https://arxiv.org/abs/1401.2452

zbMATH Keywords

diffeomorphismpartially hyperboliccenter submanifold

Mathematics Subject Classification ID

Invariant manifold theory for dynamical systems (37D10) Partially hyperbolic systems and dominated splittings (37D30) Stability theory for smooth dynamical systems (37C75)

Related Items (10)

Regularity of center manifolds via the graph transform ⋮ Homoclinic bifurcations that give rise to heterodimensional cycles near a saddle-focus equilibrium ⋮ Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms ⋮ Volume hyperbolicity and wildness ⋮ Properties of compact center-stable submanifolds ⋮ Existence of heterodimensional cycles near shilnikov loops in systems with a \(\mathbb{Z}_2\) symmetry ⋮ Hyperbolicity versus non-hyperbolic ergodic measures inside homoclinic classes ⋮ Measures of maximal entropy for surface diffeomorphisms ⋮ Existence and regularity of invariant graphs for cocycles in bundles: partial hyperbolicity case ⋮ Emergence of wandering stable components

Cites Work

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• High dimension diffeomorphisms displaying infinitely many periodic attractors
• Homoclinic tangencies and hyperbolicity for surface diffeomorphisms
• Center manifolds for invariant sets
• Diffeomorphisms with infinitely many sinks
• Generic diffeomorphisms away from homoclinic tangencies and heterodimensional cycles
• Generation of homoclinic tangencies by \(C^1\)-perturbations
• Persistence of homoclinic tangencies in higher dimensions
• Adapted metrics for dominated splittings

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