Dynamical Systems seminar - Wednesday 16 March

[math]

M A T H E M A T I C S   S E M I N A R S   2011

- DYNAMICAL SYSTEMS -


Wednesday, 16 March, at 15:00 hrs.


Dr. Denis Volk
(SISSA)


"Skew products with interval fiber"


Abstract:

Skew products over topological Markov chains naturally appear when one 
attempts to apply the methods of classical dynamical systems to random 
dynamical systems. There is also a close connection between these skew 
products and partially hyperbolic dynamical systems on smooth manifolds.

Even for the fiber dimension equal to one, we are far from understanding 
what "typical" skew products look like. During the last 30 years there 
appeared several papers studying the skew products with a circle fiber. 
I will talk about the case when the fiber is an interval, and fiber maps 
are orientation-preserving diffeomorphisms.

In the work joint with V.Kleptsyn, we developed a theorem which gives us 
a complete* description of the dynamics of typical step skew products 
(fiber map depends only on a single symbol in the base sequence). For 
generic skew products, we obtained a similar result using an additional 
assumption of partial-hyperbolic nature.

*except some subset which projects onto zero measure set in the base


VENUE: Luigi Stasi Seminar Room
(ICTP Leonardo da Vinci Building, first floor)