For more information about this meeting, contact Anatole Katok, Yakov Pesin, Dmitri Burago.

Title: | Variational construction of parabolic solutions in the N-Body Problem |

Seminar: | Center for Dynamics and Geometry Seminars |

Speaker: | Andrea Venturelli, University of Avignon |

Abstract: |

Let us consider N point masses attracting each others with a Newto-
nian force ﬁeld. A solution of the N -body problem is said to be totally
parabolic (as time go to +∞) if all mutual distances are unbounded but
the speed of every body goes to zero. For such a solution the ω-limit of
the normalized conﬁguration is contained in the set of Central Conﬁgu-
rations. We prove the following result : given a normalized minimizing
Central Conﬁguration x0 and any conﬁguration xi , there exists a par-
abolic solution starting at xi at the initial time and asymptotic to x0 .
This solution is a global minimizer of the Lagrangian action functional
and it is constructed using the direct methods of the Calculus of Vari-
ations. It is a joint work with Ezequiel Maderna (Universidad de la
Republica, Monteviedo, (UY)). |

### Room Reservation Information

Room Number: | MB106 |

Date: | 09 / 28 / 2009 |

Time: | 03:30pm - 05:30pm |