### Stable sets and unstable sets in positive entropy systems

- Series
- CDSNS Colloquium
- Time
- Monday, November 2, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Wen Huang – USTC, China and SoM, Georgia Tech

Stable sets and unstable sets of a dynamical system with positive entropy
are investigated. It is shown that in any invertible system with positive entropy,
there is a measure-theoretically ?rather big? set such that for any point from the
set, the intersection of the closure of the stable set and the closure of the
unstable set of the point has positive entropy.
Moreover, for several kinds of specific systems, the lower bound of Hausdorff
dimension of these sets is estimated. Particularly the lower bound of the Hausdorff
dimension of such sets appearing in a positive entropy diffeomorphism on a smooth
Riemannian manifold is given in terms of the metric entropy and of Lyapunov exponent.