Separatrix crossings in slow-fast Hamiltonian systems.

Applied Analysis Seminar

Meeting Details

For more information about this meeting, contact Mark Levi, Leonid Berlyand, Alexei Novikov.

Speaker: Anatoly Neishtadt, Loughboro University

Abstract: 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.

Room Reservation Information

Room Number: 106 McAllister

Date: 09/28/2010

Time: 4:00pm - 4:55pm