Friday, March 17, 2017

Asymptotic Behavior of Compact Skew-product Semiflows on Hilbert Spaces

Glória Carvalho
(Universidade do Porto)

Abstract: We consider an infinite dimensional separable Hilbert space and its family of skewproduct compact semiflows over an ergodic flow $\varphi^t : M \rightarrow M$. Assuming that $M$ is a compact Hausdorff space and $\varphi^t$ preserves a Borel regular ergodic probability $\mu$ which is positive on non-empty open sets, we will prove that there is a $\tau$-residual subset of skewproduct semiflows within which, for $\mu$ almost every $x$, either the Oseledets-Ruelle's decomposition along the orbit of $x$ is uniformly hyperbolic (in the projective space) or else the Ruelle's limit operator over the orbit of $x$ is the null operator. We prove also a $L^p$ version of this dichotomy for cocycles with a $L^p$ topology defined in infinitesimal generators set and that non-uniformly Anosov skew-products are $C^0$-dense in the family of partially hyperbolic cocycles with non-trivial unstable bundles.

Friday, March 17, 2017
Time: 14h00
Room: Sala Delta, Edificio Quelhas, ISEG