The aim of this workshop is to understand the relationship between three important singular dynamical problems: the N-body problem of celestial mechanics, and the N-vortex and N-filament problems of ideal fluid mechanics. Of all the techniques and devices used in order to tackle these problems, variational methods are an important source of new ideas and results. A crucial point for a complete understanding of the dynamic and chaotic properties of these singular systems is the description of the dynamics near collisions. In this respect it is natural and useful both from theoretical and numerical viewpoint to know, for instance, if some regularization techniques of the Celestial Mechanics could be generalized to the other two problems. Other interesting questions are related to the study of the linear stability by using symplectic techniques and in particular the Maslov index, as well as to provide some index theorems both for the ode's and for the pde's that govern the dynamics, particularly in the case of colliding solutions. We close by mentioning a challenging problem to tackle, consisting in developing a Morse theory. In this respect, due to the lack of compactness, the understanding of the asymptotic behavior of the collision solutions is fundamental. We hope that the workshop could be a starting point in order to provide an effective way to treat these milestone dynamical problems.
Workshop on Variational methods in N-body and Vortex Dynamics May 28 - June 8, 2012 Department of Mathematics and Physics "Ennio De Giorgi" Università del Salento
CARUSO, ANTONIO MARIO;PAPARELLA, Francesco;
2012-01-01
Abstract
The aim of this workshop is to understand the relationship between three important singular dynamical problems: the N-body problem of celestial mechanics, and the N-vortex and N-filament problems of ideal fluid mechanics. Of all the techniques and devices used in order to tackle these problems, variational methods are an important source of new ideas and results. A crucial point for a complete understanding of the dynamic and chaotic properties of these singular systems is the description of the dynamics near collisions. In this respect it is natural and useful both from theoretical and numerical viewpoint to know, for instance, if some regularization techniques of the Celestial Mechanics could be generalized to the other two problems. Other interesting questions are related to the study of the linear stability by using symplectic techniques and in particular the Maslov index, as well as to provide some index theorems both for the ode's and for the pde's that govern the dynamics, particularly in the case of colliding solutions. We close by mentioning a challenging problem to tackle, consisting in developing a Morse theory. In this respect, due to the lack of compactness, the understanding of the asymptotic behavior of the collision solutions is fundamental. We hope that the workshop could be a starting point in order to provide an effective way to treat these milestone dynamical problems.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
