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

Эта публикация цитируется в 512 научных статьях (всего в 516 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.

Полный текст: PDF файл (5383 kB)
Список литературы: PDF файл   HTML файл

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
\RBibitem{Sin70}
\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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