Home » Keyword index

Attractors , basins, Finite


Topology

Jacob Palis Conjecture(Finitude of Attractors)(Dynamical Systems) ★★★★

Author(s):

Conjecture   Let $ Diff^{r}(M) $ be the space of $ C^{r} $ Diffeomorphisms on the connected , compact and boundaryles manifold M and $ \chi^{r}(M) $ the space of $ C^{r} $ vector fields. There is a dense set $ D\subset Diff^{r}(M) $ ($ D\subset \chi^{r}(M) $ ) such that $ \forall f\in D $ exhibit a finite number of attractor whose basins cover Lebesgue almost all ambient space $ M $

This is a very Deep and Hard problem in Dynamical Systems . It present the dream of the dynamicist mathematicians .

Keywords: Attractors , basins, Finite

Posted by Jailton Viana
updated April 24th, 2013
add new comment
Syndicate content