Research Announcement: Partially Hyperbolic Diffeomorphisms Homotopic to the Identity on 3-Manifolds

DOI10.1007/978-3-030-38230-8_23zbMath1450.37030arXiv1801.00214OpenAlexW3016232684MaRDI QIDQ5118806

Rafael Potrie, Thomas Barthelmé, Steven H. Frankel, Sérgio R. Fenley

Publication date: 27 August 2020

Published in: 2018 MATRIX Annals (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.00214

zbMATH Keywords

classification3-manifoldspartially hyperbolic diffeomorphisms

Mathematics Subject Classification ID

Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Foliations in differential topology; geometric theory (57R30) Partially hyperbolic systems and dominated splittings (37D30)

Related Items (9)

Ergodicity and partial hyperbolicity on Seifert manifolds ⋮ Ergodicity of partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds ⋮ \(C^r\)-closing lemma for partially hyperbolic diffeomorphisms with 1D-center bundle ⋮ Global stability of discretized Anosov flows ⋮ Partial hyperbolicity and pseudo-Anosov dynamics ⋮ Dynamical incoherence for a large class of partially hyperbolic diffeomorphisms ⋮ Centralizers of partially hyperbolic diffeomorphisms in dimension 3 ⋮ Uniqueness of minimal unstable lamination for discretized Anosov flows ⋮ Classification of partially hyperbolic diffeomorphisms under some rigid conditions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A non-dynamically coherent example on \(\mathbb T^3\)
• Pseudo-Anosov flows in toroidal manifolds
• Flots d'Anosov sur les variétés graphées au sens de Waldhausen. (Anosov flows on graph manifolds in the sense of Waldhausen.)
• Partially hyperbolic diffeomorphisms of 3-manifolds with abelian fundamental groups
• Cycles for the dynamical study of foliated manifolds and complex manifolds
• Group actions on nonseparated 1-manifolds and foliations of codimension one
• Anosov flows in 3-manifolds
• Limit sets of foliations in hyperbolic 3-manifolds
• The structure of branching in Anosov flows of 3-manifolds
• Pseudo-Anosov flows and incompressible tori
• Partial hyperbolicity and robust transitivity
• The geometry of \(R\)-covered foliations
• Coarse hyperbolicity and closed orbits for quasigeodesic flows
• Counting periodic orbits of Anosov flows in free homotopy classes
• Transitive partially hyperbolic diffeomorphisms on 3-manifolds
• Seifert manifolds admitting partially hyperbolic diffeomorphisms
• Foliations, topology and geometry of 3-manifolds: \(\mathbb{R}\)-covered foliations and transverse pseudo-Anosov flows
• Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective
• Transverse foliations on the torus \(\mathbb{T}^2\) and partially hyperbolic diffeomorphisms on 3-manifolds
• Anomalous partially hyperbolic diffeomorphisms. II: Stably ergodic examples
• Foliations by planes
• Knot theory of ℝ-covered Anosov flows: homotopy versus isotopy of closed orbits
• Classification of partially hyperbolic diffeomorphisms in 3-manifolds with solvable fundamental group
• Anomalous partially hyperbolic diffeomorphisms I: dynamically coherent examples
• Flots d'Anosov sur les 3-variétés fibrées en cercles
• Uniformization of surface laminations
• On 3-manifolds that support partially hyperbolic diffeomorphisms
• Expansive flows on Seifert manifolds and on torus bundles
• Partial hyperbolicity and classification: a survey
• Caractérisation des flots d' Anosov en dimension 3 par leurs feuilletages faibles
• Partially hyperbolic dynamics in dimension three
• Pointwise partial hyperbolicity in three-dimensional nilmanifolds

This page was built for publication: Research Announcement: Partially Hyperbolic Diffeomorphisms Homotopic to the Identity on 3-Manifolds