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An example of a pathological random perturbation of the Cat Map

Published online by Cambridge University Press:  25 May 2011

TATIANA YARMOLA
TATIANA YARMOLA*
Affiliation:
Department of Mathematics, Mathematics Building, University of Maryland, College Park, MD 20742-4015, USA (email: [email protected])
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Abstract

In this paper we give an example of a random perturbation of the Cat Map that produces a ‘global statistical attractor’ in the form of a line segment. The transition probabilities for this random perturbation are smooth in some but not all directions. All initial distributions on 𝕋2 are attracted to distributions supported on this line segment.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 6 , December 2011 , pp. 1865 - 1887
Copyright
Copyright © Cambridge University Press 2011

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References

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