Partial hyperbolicity and attracting regions in 3-dimensional manifolds

Abstract

This thesis attempts to contribute to the study of differentiable dynamics both from a semi-local and global point of view. The center of study is differentiable dynamics in manifolds of dimension 3 where we are interested in the understanding of the existence and structure of attractors as well as dynamical and topological implications of the existence of a global partially hyperbolic splitting. The main contributions are new examples of dynamics without attractors where we get a quite complete description of the dynamics around some wild homoclinic classes and two results on dynamical coherence of partially hyperbolic diffeomorphisms of $\TT^3$.

PhD thesis. 294 pages, 12 figures. Advisors: Sylvain Crovisier and Martín Sambarino

References in corpus (6)

• Linearisation of conservative toral homeomorphisms
• Generic bi-Lyapunov stable homoclinic classes
• The dynamics of quasi-isometric foliations
• Perturbation de la dynamique de difféomorphismes en topologie C^1 / Perturbation of the dynamics of diffeomorphisms in the C^1-topology
• Collision, explosion and collapse of homoclinic classes
• A Hölder continuous vector field tangent to many foliations

Cited by in corpus (7)

• Classification of partially hyperbolic diffeomorphisms in 3-manifolds with solvable fundamental group
• A few remarks on partially hyperbolic diffeomorphisms of ${\mathbb{T}}^3$ isotopic to Anosov
• Topological obstructions for robustly transitive endomorphisms on surfaces
• Classification of systems with center-stable tori
• Existence of attractors for three-dimensional flows
• A new example of robustly transitive diffeomorphism
• Robust transitivity and domination for endomorphisms displaying critical points