Absolute Continuity Theorem for Random Dynamical Systems on $R^d$

Details Absolute Continuity Theorem for Random Dynamical Systems on $R^d$ Absolute Continuity Theorem for Random Dynamical Systems on $R^d$

2012-01-05

arxiv.org/abs/1201.1190v1

Mathematics

Probability

46 pages

Scientific paper

In this article we provide a proof of the so called absolute continuity theorem for random dynamical systems on $R^d$ which have an invariant probability measure. First we present the construction of local stable manifolds in this case. Then the absolute continuity theorem basically states that for any two transversal manifolds to the family of local stable manifolds the induced Lebesgue measures on these transversal manifolds are absolutely continuous under the map that transports every point on the first manifold along the local stable manifold to the second manifold, the so-called Poincar\'e map or holonomy map. In contrast to known results, we have to deal with the non-compactness of the state space and the randomness of the random dynamical system.

Affiliated with

Also associated with

No associations

Rating

Absolute Continuity Theorem for Random Dynamical Systems on $R^d$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Absolute Continuity Theorem for Random Dynamical Systems on $R^d$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Absolute Continuity Theorem for Random Dynamical Systems on $R^d$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-609977