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Seminários do IMPA

Sistemas Dinâmicos

Título
Partially Hyperbolic Diffeomorphisms with constant exponents
Expositor
Pablo D. Carrasco

UFMG
Data
Segunda-feira, 21 de janeiro de 2019, 15:30
Local
Sala 224
Resumo

Starting with a conjecture from E. Pujals in the beginning of 2000, the classification problem of partially hyperbolic diffeomorphisms on three manifolds has remained a very active research area in dynamical systems. Roughly speaking, Pujal's conjecture proposed that a three dimentional partially hyperbolic diffeomorphism could be catalogued in essentially tree large classes: a skew-product over an Anosov map, a time-one map of an Anosov flow or a DA (that is, isotopic to hyperbolic). In the recent years the conjecture was proven to be false, and efforts to salvage a general classification conjecture has also proven to be unsuccessful. This is due to the recent zoo of intricate examples that have appeared in the literature, which don't seem to fit in well defined categories.

 

The purpose of this talk is to present a simple scheme to classify partially hyperbolic diffeomorphism in a  restricted class, by assuming a strong rigid behavior on the derivative.  Nonetheless, it is plausible that these type of systems are 'building pieces' for more general classes . This is ongoing work with E. Pujals and F. Rodriguez-Hertz.