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2006 Random perturbations of two-dimensional pseudoperiodic flows
Richard B. Sowers
Illinois J. Math. 50(1-4): 853-959 (2006). DOI: 10.1215/ijm/1258059495


We consider a random perturbation of a pseudoperiodic flow on $\R^2$. The structure of such flows has been studied by Arnol'd; it contains regions where there are local Hamiltonians, and an ergodic region. Under an appropriate change of time, we identify a reduced model as the strength of the random perturbation tends to zero (along a certain subsequence). In the Hamiltonian region, arguments of Freidlin and Wentzell are used to identify a limiting graph-valued process. The ergodic region is reduced to a single point, which is "sticky". The identification of the glueing conditions which rigorously describe this stickiness follows from a perturbed test-function analysis in the ergodic region.


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Richard B. Sowers. "Random perturbations of two-dimensional pseudoperiodic flows." Illinois J. Math. 50 (1-4) 853 - 959, 2006.


Published: 2006
First available in Project Euclid: 12 November 2009

zbMATH: 1104.60016
MathSciNet: MR2247849
Digital Object Identifier: 10.1215/ijm/1258059495

Primary: 60F17
Secondary: 37A99, 37H20, 37J40

Rights: Copyright © 2006 University of Illinois at Urbana-Champaign


Vol.50 • No. 1-4 • 2006
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