Abstract

We give a detailed analytical description of the global dynamics of N points interacting through the singular logarithmic potential and subject to the following symmetry constraint: at each instant they form an orbit of the dihedral group Dl of order 2l. The main device in order to achieve our results is a technique very popular in Celestial Mechanics, usually referred to as McGehee transformation. After performing this change of coordinates that regularizes the total collision, we study the rest-points of the flow, the invariant manifolds and, with the help of a computer algebra system, we derive inter- esting information about the global dynamics for l = 2. We observe that our problem is equivalent to studying the geometry of stationary configurations of nearly-parallel vortex filaments in three dimensions in the LIA approximation.

Autore Pugliese

• Paparella Francesco

Tutti gli autori

• F. Paparella , A. Portaluri

Titolo volume/Rivista

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Anno di pubblicazione

2013

ISSN

1078-0947

ISBN

Non Disponibile

Numero di citazioni Wos

1

Ultimo Aggiornamento Citazioni

28/04/2018

Numero di citazioni Scopus

1

Ultimo Aggiornamento Citazioni

28/04/2018

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile