[Todos CMAT] Seminario de Dinámica del Viernes 21/6

Pablo Lessa lessa en cmat.edu.uy
Jue Jun 20 09:24:35 -03 2019

Hola a todas y todos,

Este *Viernes 21 de Junio* a las *14:30* en el salón de seminarios del
*IMERL* nos hablará* Thomas Barthelme* sobre *Flujos de Anosov*.



*Título:* Anosov flows in higher dimensions.

*Resumen:* Anosov flows and Anosov diffeomorphisms are the archetypical
examples of a uniformly hyperbolic dynamical systems, and, as such, have
been widely studied since their introduction by D. Anosov in the 60'. In
the past 20-30 years, a lot of work has been on the topological study of
Anosov flows in dimension 3.

There are two main takeaways from these works: First, there is an
interesting, and not fully understood, relationship between the topology of
the manifold and the dynamics of the flows that live on it. Second there is
a huge wealth of examples of Anosov flows in 3 manifolds exhibiting many
different types of properties.

For Anosov flows in higher dimensions on the other hand, almost nothing is
known. In particular, almost no examples are known: Aside from the
algebraic ones, Franks and Williams suggested a construction in 1979, but
nothing came up since then.

In this talk, I will present a partial classification result about certain
types of Anosov flows, which shows in particular that Franks and Williams
suggestion does not work. If time permits I will explain how one can modify
their construction in order to get true examples in higher dimensions.
This is joint work with C. Bonatti, A. Gogolev and F. Rodriguez Hertz
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