Email this article Realization of the acyclic Smale diagram by an omega-stable surface diffeomorfism
- Authors: Barinova M.K., Gogulina E.Y., Pochinka O.V.
- Issue: Vol 8, No 13 (2020)
- Section: Articles
- Submitted: 09.10.2025
- URL: https://ogarev-online.ru/2311-2468/article/view/322893
- ID: 322893
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Abstract
Smale diagram of ω-stable diffeomorfism is a graph, which vertices correspond to basic sets and oriented edges sequentially connect vertices of maximal chain. Smale formulated description of acceptable diagrams, which are realized by a diffeomorfism. Present paper proves that an acyclic graph is implemented by an ω-stable diffeomorfism on surface with nontrivial basic sets.
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About the authors
M. K. Barinova
Email: ogarevonline@yandex.ru
Russian Federation,
E. Yu. Gogulina
Email: ogarevonline@yandex.ru
Russian Federation,
O. V. Pochinka
Author for correspondence.
Email: ogarevonline@yandex.ru
Russian Federation,
References
- Каток А. Б., Хасселблатт Б. Введение в современную теорию динамических систем. – М.: Факториал, 1999. – 767 с.
- Смейл С. Дифференцируемые динамические системы // Успехи мат. наук. – 1970. – Т. 25, В. 1. – С. 113–185.
- Smale S. The Ω-stability theorem // Same Proceedings. – 1970. – Vol. 14. – P. 289–297.
- Williams R. The " " maps of Smale and structural stability // Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968), Amer. Math. Soc. – 1970. – P. 329–334.
- Карпов Д. В. Теория графов. – СПб.: Санкт-Петербургское отделение Математического института им. В. А. Стеклова РАН. – 2017. – 482 с.
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