Computer assisted proofs for nonsymmetric planar choreographies and for stability of the Eight

Bibliographic description

title:	Computer assisted proofs for nonsymmetric planar choreographies and for stability of the Eight
author:	Kapela Tomasz , Simo Carles
journal title:	Nonlinearity
volume:	20
issue:	5
date of publication :	2007
pages:	1241-1255
ISSN:	0951-7715
eISSN:	1361-6544
DOI:	10.1088/0951-7715/20/5/010
language:	English
journal language:	English
abstract in other languages:	We present a general method to produce computer assisted proofs of the existence of choreographies in the N-body problem. This method allows us to verify rigorously numerical data from computer simulations. As an example we use it to prove the existence of nonsymmetric choreographies with six and seven bodies. The method provides estimates for the initial conditions and for the monodromy matrix of the choreography. These data are used to show linear stability of the Eight solution restricted to the plane and zero angular momentum motions.
affiliation:	Wydział Matematyki i Informatyki : Instytut Informatyki i Matematyki Komputerowej
type:	journal article
subtype:	academic paper

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