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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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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}
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