Lobachevskii Journal of Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Lobachevskii J. Math.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Lobachevskii Journal of Mathematics, 2005, Volume 17, Pages 47–60 (Mi ljm75)  

This article is cited in 1 scientific paper (total in 1 paper)

Dynamics of finite-multivalued transformations

K. B. Igudesman

Kazan State University
Full-text PDF (142 kB) Citations (1)
References:
Abstract: 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.
Keywords: ergodic theory, dynamic system, self-similar set.
Submitted by: M. A. Malakhaltsev
Received: 08.12.2004
Bibliographic databases:
Language: English
Citation: K. B. Igudesman, “Dynamics of finite-multivalued transformations”, Lobachevskii J. Math., 17 (2005), 47–60
Citation in format AMSBIB
\Bibitem{Igu05}
\by K.~B.~Igudesman
\paper Dynamics of finite-multivalued transformations
\jour Lobachevskii J. Math.
\yr 2005
\vol 17
\pages 47--60
\mathnet{http://mi.mathnet.ru/ljm75}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2137299}
\zmath{https://zbmath.org/?q=an:1089.37001}
Linking options:
  • https://www.mathnet.ru/eng/ljm75
  • https://www.mathnet.ru/eng/ljm/v17/p47
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Lobachevskii Journal of Mathematics
    Statistics & downloads:
    Abstract page:225
    Full-text PDF :99
    References:40
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024