28 May 2002, 12.15-14.00, Store Auditorium.

Yakov Pesin (Penn State University, USA) "«Fubini's nightmare» in smooth ergodic theory"

It has been known for quite a while that  stable and unstable  invariant foliations of a hyperbolic dynamical system possesses the  crucial absolute continuity property. In other words, the classical Fibini theorem applies to these foliations. Although examples of foliations  without the absolute continuity property were known they were considered rare and insignificant. 

Recent advances in smooth ergodic theory have overturned  this point of view. Existence of pathological foliations -- the phenomenon known as Fubini's nightmare -- have been discovered  in many partially hyperbolic systems and is intimately related to nonzero Lyapunov exponents. In the recently developed stable ergodicity theory this phenomenon is considered typical in some sense. In the talk I will describe the Fubini's nightmare phenomenon and will explain how it is related to strong stochastic properties of the system.