For more information about this meeting, contact Dmitri Burago.
|Title:||Separatrix crossings in slow-fast Hamiltonian systems|
|Seminar:||Center for Dynamics and Geometry Seminars|
|Speaker:||Anatoly Neishtadt, Loughborough|
|We consider a 2 d.o.f. Hamiltonian system with one degree of freedom
corresponding to fast motion and the other corresponding to slow motion.
We assume that at frozen values of the slow variables there is a separatrix
on the phase plane of the fast variables and there is a region in the
phase space (the domain of separatrix crossings) where projections of phase
points onto the plane of the fast variables repeatedly cross the separatrix
in the process of evolution of the slow variables. For motion far from the
separatrix the "action" variable of the fast motion is an adiabatic
invariant (approximate first integral) of complete system. At separatrix
crossings the value of this adiabatic invariant undergoes jumps. We discuss
dynamical effects associated with these jumps: destruction of adiabatic
invariance, existence of many unstable periodic trajectories and,
in systems with a symmetry, existence of many small stability islands of
considerable total measure. The talk is based on joint works with
V.Sidorenko, C.Simo, D.Treschev and A.Vasiliev.
NOTE: This talk actually took place at 4.00 on Tuesday 28th september|
Room Reservation Information
|Date:||09 / 29 / 2010|
|Time:||03:35pm - 05:05pm|