For more information about this meeting, contact Svetlana Katok, Stephanie Zerby, Anatole Katok, Federico Rodriguez Hertz.
|Title:||Some geometric mechanisms for Arnold Diffusion|
|Seminar:||Center for Dynamics and Geometry Colloquium|
|Speaker:||Rafael de la Llave, Georgia Tech|
|We consider the problem whether small perturbations of integable mechanical systems
can have very large effects.
It is known that in many cases, the effcts of the perturbations average out, but there
are exceptional cases (resonances) where the perturbations do accumulate. It is a complicated
problem whether this can keep on happening because once the instability accumulates, the system
moves out of resonance.
V. Arnold discovered in 1964 some geometric structures that lead to accumulation in carefuly constructed
examples. We will present some other geometric structures that lead to the same effect in
more general systems and that can be verified in concrete systems. In particular, we will present an
application to the restricted 3 body problem. We show that, given some
conditions, for all sufficiently small
(but non-zero) values of the eccentricity, there are orbits near a Lagrange point that gain
a fixed amount of energy. These conditions (amount to the non-vanishing of an integral) are
Joint work with M. Capinski, M. Gidea, T. M-Seara|
Room Reservation Information
|Date:||10 / 28 / 2014|
|Time:||02:30pm - 03:30pm|