Geodesic
An Example of a Piecewise Linear Ergodic Polymorphism
Matematičeskie zametki, Tome 91 (2012) no. 3, pp. 323-330.

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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.
Mots-clés : polymorphism
Keywords: piecewise linear mapping, ergodicity, three-parameter family of ergodic polymorphisms. 
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P. E. Golubtsov. An Example of a Piecewise Linear Ergodic Polymorphism. Matematičeskie zametki, Tome 91 (2012) no. 3, pp. 323-330. http://geodesic.mathdoc.fr/item/MZM_2012_91_3_a0/

[1] A. M. Vershik, “Polymorphisms, Markov processes, and quasi-similarity”, Discrete Contin. Dyn. Syst., 13:5 (2005), 1305–1324 | DOI | MR | Zbl

[2] A. M. Vershik, “Mnogoznachnye otobrazheniya s invariantnoi meroi (polimorfizmy) i markovskie operatory”, Problemy teorii veroyatnostnykh raspredelenii. IV, Zap. nauchn. sem. LOMI, 72, Izd-vo «Nauka», Leningrad. otd., L., 1977, 26–61 | MR | Zbl

[3] A. Neishtadt, D. Treschev, “Polymorphisms and adiabatic chaos”, Ergodic Theory Dynam. Systems, 31:1 (2011), 259–284 | DOI | MR | Zbl