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Notícias

Palestra do Prof. Daniel Offin

Título: Lagrangian Singularities, caustics and stability of periodic orbits in Hamiltonian systems

 

Resumo: We are interested to study periodic orbits of xed energy in Hamiltonian systems. We will consider hamiltonians of kinetic plus potential type on a Riemannian manifold. It is natural when considering stability of such orbits to also look at the related notions of wavefront sets, and their caustics, which are the locus of singular points under the canonical projection into conguration space. These singular sets may contain important dynamical information concerning the periodic orbits. We begin with some elementary and not so elementary examples which help to frame the questions we propose to study. Next we discuss the connection between absolute minimization of the action and hyperbolic structures on an invariant set for a convex Lagrangian system on a compact complete manifold. Limiting cases of absolutely minimizing periodic orbits and the resulting hyperbolic structure are considered. Next we consider conditionally minimizing periodic orbits in the N-body problem with symmetry constraints. This does not fall within the category of absolutely minimizing trajectories on compact manifolds, however we show how the arguments may be modied to apply in certain cases of the N-body problem. We apply this technique to study the hyperbolic family of homographic orbits for the planar parallelogram four body problem, and the hip hop orbits of the equal mass spatial 2N body problem. We complete the course by giving a su cient condition for symmetric periodic orbits of the N-body problem to admit hyperbolic structure, using the spatio-temporal stucture of symmetric minimizing curves.

 

 

Local: Auditório do CCET

Data: 05/05/2014            

Horário: 10:00h

Notícia cadastrada em: 02/05/2014 08:09
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