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Deterministic and stochastic perturbations of area preserving flows on a two-dimensional torus

Published online by Cambridge University Press:  05 April 2011

DMITRY DOLGOPYAT ,
MARK FREIDLIN  and
LEONID KORALOV
DMITRY DOLGOPYAT
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD, USA (email: dmitry@math.umd.edu)
MARK FREIDLIN
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD, USA (email: dmitry@math.umd.edu)
LEONID KORALOV
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD, USA (email: dmitry@math.umd.edu)
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Abstract

We study deterministic and stochastic perturbations of incompressible flows on a two-dimensional torus. Even in the case of purely deterministic perturbations, the long-time behavior of such flows can be stochastic. The stochasticity is caused by instabilities near the saddle points as well as by the ergodic component of the locally Hamiltonian system on the torus.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 3 , June 2012 , pp. 899 - 918
Copyright
Copyright © Cambridge University Press 2011

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