REMINDER: ICTP Mathematics Seminar - Monday, 8 August, at 15:00 (Ali Tahzibi)/hybrid seminar

[ICTP/math - Mabilo Koutou]

ICTP MATHEMATICS SEMINARS 2022

Monday, 8 August, at 15:00 (CET)

Hybrid seminar

Venue: ICTP Luigi Stasi Seminar room (in presence)

Online
Register in advance for this meeting:
https://zoom.us/meeting/register/tJYvceqgrzwoEtGEJz4QAVNm8wHkZ82UfFEI
After registering, you will receive a confirmation email containing 
information about joining the meeting.

Title: Dirac disintegration and vanishing center exponent

Speaker: Ali Tahzibi (ICMC-Brasil)

An example due to A. Katok and also J. Yorke which appears in a note
written by J.Milnor (Fubini foiled: Katok paradoxical example in measure
theory) reveals a "pathological" behavior of a foliation by analytics
leaves in the unit square: There exists a Lebesgue full measure subset
intersecting each leaf at most one point. In other words, Lebesgue measure
disintegrates into Dirac masses.

Shub and Wilkinson found the same phenomenon for the center foliation of
some partially hyperbolic dynamics with one-dimensional center and
non-zero center exponent. Pesin and Hirayama studied a higher dimensional
version with compact center bundle and positive sum of center exponents.

In all of the above conclusions, the center leaves are compact and there
is no room for expansion. In joint work with J. Zhang we prove that for
derived from Anosov diffemorphisms (non-compact center leaves) any ergodic
measure with zero center Lyapunov exponent disintegrates into Dirac
measures.

https://indico.ictp.it/event/10024/