Regular and Chaotic Dynamics
RUS  ENG    ЖУРНАЛЫ   ПЕРСОНАЛИИ   ОРГАНИЗАЦИИ   КОНФЕРЕНЦИИ   СЕМИНАРЫ   ВИДЕОТЕКА   ПАКЕТ AMSBIB  
Общая информация
Последний выпуск
Архив
Импакт-фактор

Поиск публикаций
Поиск ссылок

RSS
Последний выпуск
Текущие выпуски
Архивные выпуски
Что такое RSS



Regul. Chaotic Dyn.:
Год:
Том:
Выпуск:
Страница:
Найти






Персональный вход:
Логин:
Пароль:
Запомнить пароль
Войти
Забыли пароль?
Регистрация


Regular and Chaotic Dynamics, 2023, том 28, выпуск 3, страницы 295–308
DOI: https://doi.org/10.1134/S1560354723030036
(Mi rcd1206)
 

On Partially Hyperbolic Diffeomorphisms and Regular Denjoy Type Homeomorphisms

Vyacheslav Z. Grines, Dmitrii I. Mints

HSE University, ul. Bolshaya Pecherskaya 25/12, 603155 Nizhny Novgorod, Russia
Список литературы:
Аннотация: In P.D. McSwiggen’s article, it was proposed Derived from Anosov type construction which leads to a partially hyperbolic diffeomorphism of the 3-torus. The nonwandering set of this diffeomorphism contains a two-dimensional attractor which consists of one-dimensional unstable manifolds of its points. The constructed diffeomorphism admits an invariant onedimensional orientable foliation such that it contains unstable manifolds of points of the attractor as its leaves. Moreover, this foliation has a global cross section (2-torus) and defines on it a Poincaré map which is a regular Denjoy type homeomorphism. Such homeomorphisms are the most natural generalization of Denjoy homeomorphisms of the circle and play an important role in the description of the dynamics of aforementioned partially hyperbolic diffeomorphisms. In particular, the topological conjugacy of corresponding Poincaré maps provides necessary conditions for the topological conjugacy of the restrictions of such partially hyperbolic diffeomorphisms to their two-dimensional attractors. The nonwandering set of each regular Denjoy type homeomorphism is a Sierpiński set and each such homeomorphism is, by definition, semiconjugate to the minimal translation of the 2-torus. We introduce a complete invariant of topological conjugacy for regular Denjoy type homeomorphisms that is characterized by the minimal translation, which is semiconjugation of the given regular Denjoy type homeomorphism, with a distinguished, no more than countable set of orbits.
Ключевые слова: topological classification, Denjoy type homeomorphism, Sierpiński set, partial hyperbolicity.
Финансовая поддержка Номер гранта
Российский научный фонд 21-11-00010
17-11-01041
Министерство науки и высшего образования Российской Федерации 075-15-2022-1101
The final version of the article was obtained with the financial support from the RSF grant (project 21-11-00010) using materials previously obtained with the financial support from the RSF grant (project 17-11-01041). In addition, the proof of Theorem 2 was obtained with the financial support from the Laboratory of Dynamical Systems and Applications NRU HSE, grant of the Ministry of Science and Higher Education of the RF, ag. No. 075-15-2022-1101.
Поступила в редакцию: 14.01.2023
Принята в печать: 01.05.2023
Реферативные базы данных:
Тип публикации: Статья
MSC: 37E30, 37D30
Язык публикации: английский
Образец цитирования: Vyacheslav Z. Grines, Dmitrii I. Mints, “On Partially Hyperbolic Diffeomorphisms and Regular Denjoy Type Homeomorphisms”, Regul. Chaotic Dyn., 28:3 (2023), 295–308
Цитирование в формате AMSBIB
\RBibitem{GriMin23}
\by Vyacheslav Z. Grines, Dmitrii I. Mints
\paper On Partially Hyperbolic Diffeomorphisms and Regular Denjoy Type Homeomorphisms
\jour Regul. Chaotic Dyn.
\yr 2023
\vol 28
\issue 3
\pages 295--308
\mathnet{http://mi.mathnet.ru/rcd1206}
\crossref{https://doi.org/10.1134/S1560354723030036}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4597756}
Образцы ссылок на эту страницу:
  • https://www.mathnet.ru/rus/rcd1206
  • https://www.mathnet.ru/rus/rcd/v28/i3/p295
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Статистика просмотров:
    Страница аннотации:86
    Список литературы:24
     
      Обратная связь:
     Пользовательское соглашение  Регистрация посетителей портала  Логотипы © Математический институт им. В. А. Стеклова РАН, 2024