Dynamical Systems Seminar

Title: Degenerate Random Perturbations of Anosov Diffeomorphisms
Speaker: Professor Tanya Yarmola
Speaker Info: University of Maryland
Brief Description:
Special Note:

I will discuss degenerate random perturbations, where transition probabilities are smooth in some but not all directions. Under such perturbations, many dynamical systems will still have invariant densities. First I will demonstrate general but not very intuitive conditions which guarantee that all invariant measures for rank 1 random perturbations of C^2 diffeomorphisms are absolutely continuous with respect to the Riemannian measure on M. For two subclasses of Anosov diffeomorphisms: hyperbolic toral automorphisms and Anosov diffeomorphisms with codimension 1 stable manifolds, the above conditions can be modified in order to relate 1-dimensional disks that support the distributions to certain foliations that arise from Anosov diffeomorphisms. Such conditions turn out to be generic, but some pathological things can also happen. I will discuss one such example, in which a simple perturbation of the Cat Map leads to a "global statistical attractor" in the form of a line segment, meaning all initial distributions are attracted to a measure supported on this line segment.
Date: Tuesday, March 10, 2009
Time: 3:00pm
Where: Lunt 105
Contact Person: Prof. Pat Hooper
Contact email: wphooper@math.northwestern.edu
Contact Phone: 847-491-2853
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