Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-27T07:10:31.805Z Has data issue: false hasContentIssue false
  • English
  • Français

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: yarmola@math.und.edu)
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Durrett, R.. Probability: Theory and Examples, 2nd edn. Duxbury Press, Belmont, CA, 1996.Google Scholar
[2]Kifer, Y.. Random Perturbations of Dynamical Systems (Progress in Probability and Statistics, 16). Birkhäuser Boston, Inc., Boston, MA, 1988.CrossRefGoogle Scholar
[3]Yarmola, T.. Degenerate random perturbations of Anosov diffeomorphisms. Ergod. Th. & Dynam. Sys. 30(3) (2010), 931–951.CrossRefGoogle Scholar
[4]Young, L.-S.. Statistical properties of dynamical systems with some hyperbolicity. Ann. of Math. (2) 147(3) (1998), 585–650.CrossRefGoogle Scholar