Dynamical Systems Seminars (Friday 7 May)

[math]

MATHEMATICS SEMINARS 2010/DYNAMICAL SYSTEMS

Friday, 7 May

Venue: Luigi Stasi Seminar Room (ICTP Leonardo Building, first floor)

14:00  Professor Yakov Pesin (PSU, USA)
15:30  Professor Andrei Agrachev (SISSA, Italy)

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Professor Yakov Pesin
(Pennsylvania State University, University Park, USA)


"Pugh-Shub Stable Ergodicity, Partial Hyperbolicity and Lyapunov Exponents".

Abstract:
This talk is a survey of recent advances in the Pugh-Shub
stable ergodicity theory for partially hyperbolic diffeomorphisms. I
describe two "competing" methods to show that a given partially
hyperbolic diffeomorphism  is stably ergodic (i.e., it is ergodic along
with any of its sufficiently small perturbations). One of them relates
the problem to the global estimates of the action of the system along
its central direction while another one deals with a more delicate
estimates using Lyapunov exponents in the central direction."

***

Professor Andrei Agrachev
(SISSA, Italy)

"Invariant Lagrange Submanifolds of Dissipative Systems"

Abstract:
Given a Riemannian manifold M and “mechanical” Hamiltonian func-
tion H on T* M we construct invariant Lagrange submanifolds of 
dissipative systems on T* M whose cooordinate presentation has the form

q' = dH/dp(p,q) , p' = -aH/dq(p,q)-ap

where a is a positive constant.
The construction uses the curvature of the flows on the cotangent bundle
and ideas of the partially hyperbolic dynamics.