Continuous Morse-Smale flows with three equilibrium positions

Zhuzhoma, E. V.; Medvedev, Vladislav Sergeevich

doi:10.4213/sm8565

Cited by 16 publications

(1 citation statement)

References 23 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Проблема топологической классификации динамических систем Морса-Смейла на многообразиях размерности 4 и выше, отличных от сферы, рассматривалась в [22] для потоков и каскадов с неблуждающим множеством, состоящим в точности из трех и четырех неподвижных точек.…”

unclassified

О реализации классов топологической сопряженности каскадов Морса-Смейла на сфере $S^n$

Гринес¹,

Grines

Gurevich³

et al. 2020

Trudy Matematicheskogo Instituta imeni V.A. Steklova

Self Cite

View full text Add to dashboard Cite

Рассматривается класс $G(S^n)$ сохраняющих ориентацию диффеоморфизмов Морса-Смейла, заданных на сфере $S^n$ размерности $n\geq 4$, в предположении, что инвариантные многообразия различных седловых периодических точек не пересекаются. Для диффеоморфизмов из этого класса описан алгоритм реализации всех классов топологической сопряженности.

show abstract

unclassified

О реализации классов топологической сопряженности каскадов Морса-Смейла на сфере $S^n$

Гринес¹,

Grines

Gurevich³

et al. 2020

Trudy Matematicheskogo Instituta imeni V.A. Steklova

Self Cite

View full text Add to dashboard Cite

show abstract

On Embedding of the Morse–Smale Diffeomorphisms in a Topological Flow

2022

View full text Add to dashboard Cite

This review presents the results of recent years on solving of the Palis problem on finding necessary and sufficient conditions for the embedding of Morse-Smale cascades in topological flows. To date, the problem has been solved by Palis for Morse-Smale diffeomorphisms given on manifolds of dimension two. The result for the circle is a trivial exercise. In dimensions three and higher new effects arise related to the possibility of wild embeddings of closures of invariant manifolds of saddle periodic points that leads to additional obstacles for Morse-Smale diffeomorphisms to be embedded in topological flows. The progress achieved in solving of Palis's problem in dimension three is associated with the recently obtained complete topological classification of Morse-Smale diffeomorphisms on threedimensional manifolds and the introduction of new invariants describing the embedding of separatrices of saddle periodic points in a supporting manifold. The transition to a higher dimension requires the latest results from the topology of manifolds. The necessary topological information, which plays key roles in the proofs, is also presented in the survey.

show abstract

Necessary and sufficient conditions for the conjugacy of Smale regular homeomorphisms

Zhuzhoma¹,

Medvedev²

2021

Sb. Math.

View full text Add to dashboard Cite

The class of Smale regular homeomorphisms of closed topological manifolds, with nonwandering set consisting of a finite number of periodic orbits of hyperbolic type, is considered. This class contains the Morse-Smale diffeomorphisms of smooth closed manifolds. For two Smale regular homomorphisms necessary and sufficient conditions for being conjugate are presented. Bibliography: 26 titles.

show abstract

Continuous Morse-Smale flows with three equilibrium positions

Cited by 16 publications

References 23 publications

О реализации классов топологической сопряженности каскадов Морса-Смейла на сфере $S^n$

О реализации классов топологической сопряженности каскадов Морса-Смейла на сфере $S^n$

On Embedding of the Morse–Smale Diffeomorphisms in a Topological Flow

Necessary and sufficient conditions for the conjugacy of Smale regular homeomorphisms

Contact Info

Product

Resources

About