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Matematicheskie Zametki, 2012, Volume 91, Issue 3, Pages 323–330
DOI: https://doi.org/10.4213/mzm8956 (Mi mzm8956) 		 
This article is cited in 1 scientific paper (total in 1 paper)

An Example of a Piecewise Linear Ergodic Polymorphism

P. E. Golubtsov

M. V. Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm8956
Abstract: We consider dynamical systems introduced by Vershik and called polymorphisms. In particular, such systems encompass the class of multivalued mappings of a closed interval onto itself which have an invariant measure. Polymorphisms arise in different areas of mathematics and mechanics, for example, in the problem of the destruction of the adiabatic invariant. We are concerned with the ergodic properties of polymorphisms. The first section deals with the main notions. In Secs. 2 and 3, we consider an example of a three-parameter family of ergodic polymorphisms formed by piecewise linear mappings.
Keywords: polymorphism, piecewise linear mapping, ergodicity, three-parameter family of ergodic polymorphisms.
Received: 21.04.2009
Revised: 01.10.2010
English version:
Mathematical Notes, 2012, Volume 91, Issue 3, Pages 311–317
DOI: https://doi.org/10.1134/S0001434612030017
Bibliographic databases:
Document Type: Article
UDC: 531.01
Language: Russian
Citation: P. E. Golubtsov, “An Example of a Piecewise Linear Ergodic Polymorphism”, Mat. Zametki, 91:3 (2012), 323–330; Math. Notes, 91:3 (2012), 311–317
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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