http://openproblemgarden.org/op/jacob_palis_conjecture_finitude_of_attractors_dynamical_systems Comments for " Jacob Palis Conjecture(Finitude of Attractors)(Dynamical Systems)" en http://openproblemgarden.org/op/jacob_palis_conjecture_finitude_of_attractors_dynamical_systems <table cellspacing="10"> <tr> <td> Author(s): <a href="/kpz_equation_central_limit_theorem"></a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/topology">Topology</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; Let <img class="teximage" src="/files/tex/96b7458da5816649d7f2ad399ef03fb416359d46.png" alt="$ Diff^{r}(M) $" /> be the space of <img class="teximage" src="/files/tex/b66404b2329b94aa018acb2481e504cd18fcd638.png" alt="$ C^{r} $" /> Diffeomorphisms on the connected , compact and boundaryles manifold M and <img class="teximage" src="/files/tex/60a0032cb74d2f8ef538590ff6e92abecc056eec.png" alt="$ \chi^{r}(M) $" /> the space of <img class="teximage" src="/files/tex/b66404b2329b94aa018acb2481e504cd18fcd638.png" alt="$ C^{r} $" /> vector fields. There is a dense set <img class="teximage" src="/files/tex/ebb61bcfdb969ad1b3cfd893afb858ee13d86f5a.png" alt="$ D\subset Diff^{r}(M) $" /> (<img class="teximage" src="/files/tex/a9b664fbb7fb5dd089d5f67b082350ac8f9cef3f.png" alt="$ D\subset \chi^{r}(M) $" /> ) such that <img class="teximage" src="/files/tex/4a046aee22105c97503f4ec3488a0dcb4dcdc75f.png" alt="$ \forall f\in D $" /> exhibit a finite number of attractor whose basins cover Lebesgue almost all ambient space <img class="teximage" src="/files/tex/3f02401f624e31ef8679d3c3628c1f310058f388.png" alt="$ M $" /> </div> <p> This is a very Deep and Hard problem in Dynamical Systems . It present the dream of the dynamicist mathematicians .</p> </tr></td> </table> </td> </tr> </table> Attractors , basins, Finite Topology http://openproblemgarden.org/op/jacob_palis_conjecture_finitude_of_attractors_dynamical_systems#comment Wed, 24 Apr 2013 19:06:25 +0200 Jailton Viana 48770 at http://openproblemgarden.org