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Lobachevskii Journal of Mathematics, 2005, том 17, страницы 47–60
(Mi ljm75)
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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Dynamics of finite-multivalued transformations
K. B. Igudesman Kazan State University
Аннотация:
We consider a transformation of a normalized measure space such that the image of any point is a finite set. We call such a transformation an $m$-transformation. In this case the orbit of any point looks like a tree. In the study of $m$-transformations we are interested in the properties of the trees. An $m$-transformation generates a stochastic kernel and a new measure. Using these objects, we introduce analogies of some main concept of ergodic theory: ergodicity, Koopman and Frobenius–Perron operators etc. We prove ergodic theorems and consider examples. We also indicate possible applications to fractal geometry and give a generalization of our construction.
Ключевые слова:
ergodic theory, dynamic system, self-similar set.
Образец цитирования:
K. B. Igudesman, “Dynamics of finite-multivalued transformations”, Lobachevskii J. Math., 17 (2005), 47–60
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/ljm75 https://www.mathnet.ru/rus/ljm/v17/p47
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Страница аннотации: | 225 | PDF полного текста: | 99 | Список литературы: | 40 |
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