A combinatorial invariant of gradient-like flows on a connected sum of $\mathbb{S}^{n-1}\times\mathbb{S}^1$

DOI10.4213/sm9761eMaRDI QIDQ6188994

E. Ya. Gurevich, Vyacheslav Z. Grines

Publication date: 12 January 2024

Published in: Sbornik: Mathematics (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/sm9761

zbMATH Keywords

topological classificationMorse-Smale flowgradient-like flow

Mathematics Subject Classification ID

Stability of topological dynamical systems (37B25) Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Generic properties, structural stability of dynamical systems (37C20) Gradient-like behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems (37B35) Index theory for dynamical systems, Morse-Conley indices (37B30) Combinatorial dynamics (types of periodic orbits) (37E15) Stability theory for smooth dynamical systems (37C75)

Cites Work

• Topological classification of Morse-Smale diffeomorphisms without heteroclinic intersections
• Morse index of saddle equilibria of gradient-like flows on connected sums of \(\mathbb{S}^{n-1}\times \mathbb{S}^1\)
• On realization of topological conjugacy classes of Morse-Smale cascades on the sphere \(S^n\)
• On gradient dynamical systems
• Stable homeomorphisms and the annulus conjecture
• Stable structures on manifolds. I: Homeomorphismus of \(S^ n\). II: Stable manifolds. III: Applications
• Morse inequalities for a dynamical system
• Differential Topology
• Classification of Morse-Smale flows on two-dimensional manifolds
• On topological classification of Morse–Smale diffeomorphisms on the sphere S ⁿ (n > 3)
• A proof of the generalized Schoenflies theorem
• On the work of L. V. Keldysh and her seminar
• On the Group of All Homeomorphisms of a Manifold
• Differentiable dynamical systems
• Energy Functions for Morse Smale Systems
• NECESSARY AND SUFFICIENT CONDITIONS FOR TOPOLOGICAL EQUIVALENCE OF THREE-DIMENSIONAL MORSE-SMALE DYNAMICAL SYSTEMS WITH A FINITE NUMBER OF SINGULAR TRAJECTORIES
• Locally flat imbeddings of topological manifolds
• Three-manifolds admitting Morse-Smale diffeomorphisms without heteroclinic curves.
• 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
• Unnamed Item

This page was built for publication: A combinatorial invariant of gradient-like flows on a connected sum of $\mathbb{S}^{n-1}\times\mathbb{S}^1$