Global attractor and repeller of Morse-Smale diffeomorphisms

DOI10.1134/S0081543810040097zbMath1302.37021OpenAlexW2020183668MaRDI QIDQ483156

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

Publication date: 16 December 2014

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

Full work available at URL: https://doi.org/10.1134/s0081543810040097

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Morse-Smale systems (37D15)

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Cites Work

• Unnamed Item
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• Peixoto graph of Morse-Smale diffeomorphisms on manifolds of dimension greater than three
• Global dynamics of Morse-Smale systems
• A mildly wild imbedding of an \(n\)-frame
• Generalized Poincaré's conjecture in dimensions greater than four
• The topology of four-dimensional manifolds
• New relations for Morse-Smale flows and diffeomorphism
• On Morse-Smale diffeomorphisms on manifolds of dimension higher than three
• Beginner's course in topology. Geometric chapters. Transl. from the Russian by A. Iacob
• Wild unstable manifolds
• Constructing structurally stable diffeomorphisms
• Homology theory and dynamical systems
• Topological classification of gradient-like diffeomorphisms on 3-manifolds.
• On the topological classification of gradient-like diffeomorphisms without heteroclinic curves on three-dimensional manifolds.
• Knots as topological invariants for gradient-like diffeomorphisms of the sphere \(S^3\)
• On the Morse-Smale diffeomorphisms with four periodic points on closed orientable manifolds.
• Diffeomorphisms with infinitely many sinks
• Stable homeomorphisms and the annulus conjecture
• On Morse-Smale dynamical systems
• Some wild cells and spheres in three-dimensional space
• Two-dimensional links and diffeomorphisms on 3-manifolds
• CLASSIFICATION OF MORSE-SMALE DIFFEOMORPHISMS WITH THE CHAIN OF SADDLES ON 3-MANIFOLDS
• Morse inequalities for a dynamical system
• Self-indexing energy function for Morse-Smale diffeomorphisms on 3-manifolds
• Polyhedral homotopy-spheres
• Classification of gradient-like flows on dimensions two and three
• New relations for Morse-Smale systems with trivially embedded one-dimensional separatrices
• n-Frames in Euclidean k-Space
• On the work of L. V. Keldysh and her seminar
• On the triangulation of manifolds and the Hauptvermutung
• Differentiable dynamical systems
• The generalised Poincaré conjecture

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