Speaker: Amadeu Delshams (Universitat Politecnica de Catalunya)

Title of the talk: Geometrical methods for global instability in mechanical systems

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 as well as some problems from celestial mechanics give rise to a priori chaotic Hamiltonian systems, 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 conference is based on joint work with Gemma Huguet, Rafael de la Llave and Tere M. Seara. Related papers can be found in http://www.ma1.upc.edu/~amadeu.