[Binghamton Geometry/Topology Seminar] Feb 9

[Dmytro Savchuk]

                   BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR

*Date:*  Thursday, Feb 9, 2012

*Time:*  2:50-3:50pm
*Place:*  Library North 2205 followed by coffee/tea in the Anderson Reading
Room.

*Speaker:* Raul Ures (IMERL, Montevideo)

*Title: **Partial hyperbolicity and ergodicity in dimension 3*
*
Abstract:* A dynamical system is partially hyperbolic if it has three
invariant directions E^s, E^c and E^u, being E^s uniformly contracting, E^u
uniformly expanding while E^c has an intermediate behavior. The study of
partially hyperbolic systems has been one of the most active topics in
dynamics in the last two decades. The purpose of this talk will be to
present the state of the art in the study of the ergodicity of conservative
partially hyperbolic diffeomorphisms on three dimensional manifolds.
Interestingly, 3-dimensional topology is a crucial ingredient in the study
of such systems. In a previous work (joint with Jana and Federico Rodriguez
Hertz) we proved the Pugh-Shub conjecture for partially hyperbolic
diffeomorphisms with 1-dimensional center, i.e. stably ergodic
diffeomorphisms are dense among the partially hyperbolic ones. In
subsequent results, we obtained, jointly with the same co-authors, a more
accurate description of this abundance of ergodicity in dimension three. We
will describe these results, some recent advances and the main open
problems and conjectures on the subject.
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