This work of A. B. was supported in part by NSF grant number DMS-1109532, that of V. M. and M. S. J. by DMS-1109638, and that of E.S.T. by DMS-1009950, DMS-1109640 and DMS-1109645, as well as the Minerva Stiftung/Foundation.
Let φ be a white noise RDS on a complete, d-dimensional smooth Riemannian manifold E with respect to an ergodic metric dynamical system (Ω,P,θ) and let (Pt) be the associated Markovian semigroup. Further assume that φt(ω,⋅)∈C1,δloc for some δ>0 and …
The authors would like to thank Tom Liggett, Noam Berger and Elchanan Mossel for many useful discussions.
In this section we will finally prove the main theorems. In order to obtain the equivalence of regularity and domination as stated in Theorem 1.2 we will argue with approximation of the unstable and stable directions by rational frequencies and conv…
It is a pleasure to thank my dissertation advisor, Anton Gorodetski, for many helpful discussions and for a period of financial support during which this project was conceived and completed.
For the purpose of analyzing the stability of equilibria it is more convenient to use a slightly different parametrization of the manifold of curves about a fixed steady-state. Any small enough ρ∈V can be described using the coordinates
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