Я. Г. Синай, “Динамические системы с упругими отражениями. Эргодические свойства рассеивающих бильярдов”, УМН, 25:2(152) (1970), 141–192; Russian Math. Surveys, 25:2 (1970), 137

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УМН, 1970, том 25, выпуск 2(152), страницы 141–192 (Mi umn5322)

Эта публикация цитируется в 513 научных статьях (всего в 517 статьях)

Динамические системы с упругими отражениями. Эргодические свойства рассеивающих бильярдов

Я. Г. Синай

Аннотация: В статье рассматриваются динамические системы, порожденные движением материальной точки в областях со строго выпуклым внутрь краем, т. е. в таких, что оператор второй квадратичной формы в каждой точке границы области отрицательно определенный, если считать край оснащенным полем внутренних нормалей. Доказывается, что такие системы эргодичныи являются $K$-системами. В основе метода исследования лежит построение трансверсальных слоений для таких систем и изучение свойств этих слоений.

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Англоязычная версия:
Russian Mathematical Surveys, 1970, 25:2, 137–189

Реферативные базы данных:

УДК: 518.25
MSC: 37N05, 37Axx, 37D50, 37D40
Поступила в редакцию: 11.12.1969

Образец цитирования: Я. Г. Синай, “Динамические системы с упругими отражениями. Эргодические свойства рассеивающих бильярдов”, УМН, 25:2(152) (1970), 141–192; Russian Math. Surveys, 25:2 (1970), 137–189

Цитирование в формате AMSBIB

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\by Я.~Г.~Синай

\paper Динамические системы с~упругими отражениями. Эргодические

свойства рассеивающих бильярдов

\jour УМН

\yr 1970

\vol 25

\issue 2(152)

\pages 141--192

\mathnet{http://mi.mathnet.ru/umn5322}

\mathscinet{http://www.ams.org/mathscinet-getitem?mr=274721}

\zmath{https://zbmath.org/?q=an:0252.58005|0263.58011}

\transl

\jour Russian Math. Surveys

\yr 1970

\vol 25

\issue 2

\pages 137--189

\crossref{https://doi.org/10.1070/RM1970v025n02ABEH003794}

Образцы ссылок на эту страницу:

http://mi.mathnet.ru/umn5322

http://mi.mathnet.ru/rus/umn/v25/i2/p141

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