Starts 8 Aug 2022 15:00
Ends 8 Aug 2022 16:00
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Dirac disintegration and vanishing center exponent
Online
Leonardo Building - Luigi Stasi Seminar Room
Register in advance for this meeting:
https://zoom.us/meeting/register/tJYvceqgrzwoEtGEJz4QAVNm8wHkZ82UfFEI
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Abstract: 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://zoom.us/meeting/register/tJYvceqgrzwoEtGEJz4QAVNm8wHkZ82UfFEI
After registering, you will receive a confirmation email containing
information about joining the meeting.
Abstract: 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.
This will be hybrid seminar. All are very welcome to join either online or in person. Venue: Luigi Stasi Seminar (ICTP Leonardo Da Vinci Building), for those wishing to attend in person.