On surface attractors and repellers in 3-manifolds

DOI10.1007/s11006-005-0181-1zbMath1107.37024arXivmath/0412317OpenAlexW2952677088MaRDI QIDQ2508746

V. S. Medvedev, Evgeny Zhuzhoma, Vyacheslav Z. Grines

Publication date: 20 October 2006

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0412317

zbMATH Keywords

attractordiscrete dynamical systemrepellerAnosov diffeomorphismthree-dimensional manifoldtame surface

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20)

Related Items (15)

Dynamical Systems with Nontrivially Recurrent Invariant Manifolds ⋮ The topological classification of structurally stable 3-diffeomorphisms with two-dimensional basic sets ⋮ On the number of heteroclinic curves of diffeomorphisms with surface dynamics ⋮ Rough diffeomorphisms with basic sets of codimension one ⋮ Dynamics of three-dimensional A-diffeomorphisms with two-dimensional attractors and repellers ⋮ There are no structural stable axiom a 3-diffeomorphisms with dynamics ``one-dimensional surfaced attractor-repeller ⋮ On a structure of non-wandering set of an \(\Omega\)-stable 3-diffeomorphism possessing a hyperbolic attractor ⋮ On partially hyperbolic diffeomorphisms and regular Denjoy type homeomorphisms ⋮ On a topological classification of diffeomorphisms on 3-manifolds with two-dimensional surface attractors and repellers ⋮ The constructing of energy functions for \(\Omega \)-stable diffeomorphisms on 2- and 3-manifolds ⋮ Dynamics of 3-homeomorphisms with two-dimensional attractors and repellers ⋮ Around Anosov-Weil Theory ⋮ On the dynamical coherence of structurally stable 3-diffeomorphisms ⋮ Surface basic sets with wildly embedded supporting surfaces ⋮ Topological classification of Morse-Smale diffeomorphisms on \(3\)-manifolds

Cites Work

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• A simple proof of the Franks–Newhouse theorem on codimension-one Anosov diffeomorphisms
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• 3-manifolds that admit knotted solenoids as attractors
• On structurally stable diffeomorphisms with codimension one expanding attractors
• Anosov Diffeomorphisms on Tori
• Differentiable dynamical systems
• On Codimension One Anosov Diffeomorphisms
• Periodic Points and Measures for Axiom a Diffeomorphisms
• THE TOPOLOGY OF BASIS SETS FOR SMALE DIFFEOMORPHISMS
• Expanding attractors
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