Classification of Morse-Smale diffeomorphisms with one-dimensional set of unstable separatrices

DOI10.1134/S0081543810030053zbMath1226.37012MaRDI QIDQ630201

E. Ya. Gurevich, V. S. Medvedev, Vyacheslav Z. Grines

Publication date: 17 March 2011

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

zbMATH Keywords

heteroclinic intersectionsorientation-preserving Morse-Smale diffeomorphismsunstable separatrices

Mathematics Subject Classification ID

Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Dynamical systems involving smooth mappings and diffeomorphisms (37C05) Morse-Smale systems (37D15)

Related Items (10)

High-dimensional Morse-Smale systems with king-saddles ⋮ Efficient algorithms for the recognition of topologically conjugate gradient-like diffeomorhisms ⋮ On realization of topological conjugacy classes of Morse-Smale cascades on the sphere \(S^n\) ⋮ On topological classification of Morse–Smale diffeomorphisms on the sphere S ⁿ (n > 3) ⋮ On topological classification of gradient-like flows on an \(n\)-sphere in the sense of topological conjugacy ⋮ An analog of Smale's theorem for homeomorphisms with regular dynamics ⋮ Topological classification of Morse-Smale diffeomorphisms without heteroclinic intersections ⋮ Classification of Morse–Smale systems and topological structure of the underlying manifolds ⋮ A combinatorial invariant of Morse-Smale diffeomorphisms without heteroclinic intersections on the sphere \(S^n\), \(n\geq 4\) ⋮ Morse-Smale systems and topological structure of carrier manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Peixoto graph of Morse-Smale diffeomorphisms on manifolds of dimension greater than three
• Classification of Morse-Smale diffeomorphisms with finite sets of heteroclinic orbits on 3-manifolds
• On Morse-Smale diffeomorphisms on manifolds of dimension higher than three
• On 4-dimensional s-cobordisms
• On low dimensional s-cobordisms
• Irrationality and the h-cobordism conjecture
• 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 \(S^3\)
• 4-manifold topology. I: Subexponential groups
• On combinatorial isotopy
• On irreducible 3-manifolds which are sufficiently large
• The Whitehead group of a polynomial extension
• Two-dimensional links and diffeomorphisms on 3-manifolds
• Topological Invariance of Whitehead Torsion
• Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88)
• New relations for Morse-Smale systems with trivially embedded one-dimensional separatrices
• LOCALLY NICE EMBEDDINGS IN CODIMENSION THREE
• Differentiable dynamical systems
• The Units of Group-Rings
• Simple Homotopy Types
• Locally flat imbeddings of topological manifolds

This page was built for publication: Classification of Morse-Smale diffeomorphisms with one-dimensional set of unstable separatrices