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Polymorphisms and adiabatic chaos

Published online by Cambridge University Press:  02 February 2010

A. NEISHTADT  and
D. TRESCHEV
A. NEISHTADT
Affiliation:
Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK Space Research Institute, Profsoyuznaya 84/32, Moscow, 117997, Russia
D. TRESCHEV
Affiliation:
Steklov Mathematical Institute, Gubkina 8, Moscow, 119991, Russia
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Abstract

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At the end of the last century Vershik introduced some dynamical systems, called polymorphisms. Systems of this kind are multivalued self-maps of an interval, where (roughly speaking) each branch has some probability. By definition, the standard Lebesgue measure should be invariant. Unexpectedly, some class of polymorphisms appeared in the problem of destruction of an adiabatic invariant after a multiple passage through a separatrix. We discuss ergodic properties of polymorphisms from this class.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 1 , February 2011 , pp. 259 - 284
Copyright
Copyright © Cambridge University Press 2010

References

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