[Todos CMAT] Seminario Dinámica- Sylvain Crovisier

[Rafael Potrie]

Hola todos,

Este *Viernes 5/12* a las *14.30* en el *IMERL* recibimos a Sylvain
Crovisier <http://www.math.u-psud.fr/~crovisie/> (CNRS-Univ. Paris-Sud) que
hablará sobre* "On the density of singular hyperbolic three-dimensional
vector fields"*. Abajo encontrarán un resumen.

Son todos bienvenidos,


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On the density of singular hyperbolic three-dimensional vector fields

We will discuss vector fields on three-dimensional manifolds.
For an open class of systems - the singular hyperbolic ones - the dynamics
decomposes into finitely many transitive pieces (this includes hyperbolic
basic sets and Lorenz attractors).
On the other hand it is known that some simple bifurcations - the
homoclinic tangencies - may generate systems with infinitely many disjoint
attractors.
Palis has conjectured that systems exhibiting either a homoclinic tangency
or satisfying the singular hyperbolicity form a dense subset of the space of
C^1 vector fields. We propose a proof of this conjecture. It requires to
extend to local fibered flows the Mañé and Pujals-Sambarino's theorems
about the uniform
contraction of one-dimensional dominated bundles.
This is a joint work with D. Yang.
-- 
Rafael Potrie
rafaelpotrie en gmail.com
http://www.cmat.edu.uy/~rpotrie/
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