Topological classification of Morse-Smale diffeomorphisms on \(3\)-manifolds

DOI10.1215/00127094-2019-0019zbMath1435.37050arXiv1710.08292OpenAlexW3101622532MaRDI QIDQ2336098

Christian Bonatti, Olga V. Pochinka, Vyacheslav Z. Grines

Publication date: 18 November 2019

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

Full work available at URL: https://arxiv.org/abs/1710.08292

zbMATH Keywords

Morse-Smale diffeomorphismtopological classification

Mathematics Subject Classification ID

Stability of topological dynamical systems (37B25) Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Stability theory for smooth dynamical systems (37C75) Wild embeddings (57M30) Morse-Smale systems (37D15)

Related Items

Components of stable isotopy connectedness of Morse-Smale diffeomorphisms, High-dimensional Morse-Smale systems with king-saddles, On the realisability of Smale orders, Link as a complete invariant of Morse-Smale 3-diffeomorphisms, Bifurcation of a disappearance of a non-compact heteroclinic curve, Bicolor Graph of Morse-Smale Cascades on Manifolds of Dimension Three, Morse-Smale surfaced diffeomorphisms with orientable heteroclinic, Knot as a complete invariant of a Morse-Smale 3-diffeomorphism with four fixed points;Узел как полный инвариант 3-диффеоморфизмов Морса-Смейла с четырьмя неподвижными точками, Knotted toroidal sets, attractors and incompressible surfaces, On 4-dimensional flows with wildly embedded invariant manifolds of a periodic orbit, On topological classification of Morse–Smale diffeomorphisms on the sphere S ⁿ (n > 3), Periods of Morse-Smale diffeomorphisms on \(\mathbb{S}^n, \mathbb{S}^m \times \mathbb{S}^n, \mathbb{C}\mathbf{P}^n\) and \(\mathbb{H}\mathbf{P}^n\), On embedding of the Morse-Smale diffeomorphisms in a topological flow

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dynamical systems on 2- and 3-manifolds
• Global attractor and repeller of Morse-Smale diffeomorphisms
• 3-manifolds which are orbit spaces of diffeomorphisms
• Wild unstable manifolds
• Topological classification of Morse-Smale diffeomorphisms with finite set of heteroclinic trajectories on surfaces
• Topological classification of gradient-like diffeomorphisms on 3-manifolds.
• Knots as topological invariants for gradient-like diffeomorphisms of the sphere \(S^3\)
• Realization of Morse-Smale diffeomorphisms on 3-manifolds
• Morse-Smale vector fields without closed trajectories on three-dimensional manifolds.
• On surface attractors and repellers in 3-manifolds
• On gradient dynamical systems
• Curves von 2-manifolds and isotopies
• On Morse-Smale dynamical systems
• Some wild cells and spheres in three-dimensional space
• Local density of diffeomorphisms with large centralizers
• Embeddings of surfaces in euclidean three-space
• On the topological classification of structurally stable diffeomorphisms of surfaces with one-dimensional attractors and repellers
• On embedding a Morse-Smale diffeomorphism on a 3-manifold in a topological flow
• Morse-Smale cascades on 3-manifolds
• Topological classification of Morse–Smale diffeomorphisms without heteroclinic curves on 3-manifolds
• Differentiable dynamical systems
• A Characterization of Tame Curves in Three-Space
• Three-manifolds admitting Morse-Smale diffeomorphisms without heteroclinic curves.