
Jacob Palis Conjecture(Finitude of Attractors)(Dynamical Systems)
Conjecture Let
be the space of
Diffeomorphisms on the connected , compact and boundaryles manifold M and
the space of
vector fields. There is a dense set
(
) such that
exhibit a finite number of attractor whose basins cover Lebesgue almost all ambient space








This is a very Deep and Hard problem in Dynamical Systems . It present the dream of the dynamicist mathematicians .
Definition : A set is an attractor for a Diffeomorphism (or a flow ) if it is invariant , transitive and the basin of attraction
has positive Lebesgue Measure.
Bibliography
Bonatti C, Diaz L.; Viana M.; Dynamics beyond uniform hyperbolicity , Springer[Encyclopaedia of Mathematics Sciences ], Volume 102, 2005
* indicates original appearance(s) of problem.