Global instability in mechanical systems via geometrical methods

Meeting Details

For more information about this meeting, contact Sergei Tabachnikov.

Speaker: Amadeu Delshams, Universitat Politecnica de Catalunya

Abstract: I will describe two different settings where geometrical methods can be applied to detect (global) instability in mechanical systems: a priori chaotic and a priori unstable Hamiltonian systems. A very wide class of geodesic flows in any dimension plus a quasi-periodic perturbation give rise to a priori chaotic Hamiltonian system, whereas a priori unstable Hamiltonian systems take place in considering periodic perturbations of a (or some) pendulum plus a (or some) rotor. In both cases, there is a very big invariant object called NHIM (normally hyperbolic invariant manifold), which apart from its inner dynamics, possesses an outer dynamics, due to the transversal intersection of its associated unstable and stable invariant manifolds, which is described by the so called scattering map. The combination of both dynamics along the NHIM gives rise to chaotic and unstable global behavior. This talk is based on joint work with Gemma Huguet, Rafael de la Llave and Tere M. Seara.

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Room Reservation Information

Room Number: 114 McAllister

Date: 10/28/2010

Time: 4:00pm - 5:00pm