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

Nonlinearity

Volumn 20, Issue 5, 2007, Pages 1241-1255

  Kapela, Tomasz ^a   Simó, Carles ^b  

^a JAGIELLONIAN UNIVERSITY   (Poland)

^b UNIVERSITY OF BARCELONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34249326952     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/20/5/010     Document Type: Article

References (13)

1. CAPD-Computer assisted proofs in dynamics, a package for rigorous numerics, http://capd.wsb-nlu.edu.pl/
2. Hénon M private communication
3. Krawczyk R 1969 Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken Computing 4 187-201
4. Kapela T 2003 N-body choreographies with a reflectional symmetry-computer assisted existence proofs EQUADIFF 2003, Proc. Int. Conf. on Differential Equations (Hasselt, Belgium, 22-26 July 2003) pp 999-1005
5. Kapela T and Zgliczyński P 2003 The existence of simple choreographies for the N-body problem-a computer assisted proof Nonlinearity 16 1899-918
6. Kapela T http://www.ii.uj.edu.pl/∼kapela/
7. McLaughlin J 2001 New simple choreographies of the N-body problem Preprint
8. Simó C Choreographies of the N-body problem http://www.maia.ub.es/ dsg/nbody
9. Simó C 2001 Periodic orbits of the planar N-body problem with equal masses and all bodies on the same path The Restless Universe: Applications of N-Body Gravitational Dynamics to Planetary, Stellar and Galactic Systems ed B Steves and A Maciejewski (Bristol: IOP Publishing) pp 265-84 (NATO Advanced Study Institute) see also http://www.maia.ub.es/dsg/2001/
10. Simó C 2001 New families of solutions in N-body problems European Congr. Mathematics (Barcelona, 2000) Progr. Math. 201 101-15 vol I (Basel: Birkhäuser)
11. Simó C 2002 Dynamical properties of the figure eight solution of the three-body problem Celestial Mechanics (Evanston, IL, 1999) Contemp. Math. 292 209-28 (Providence, RI: American Mathematical Society)
12. Stoer J and Bulirsch R 1983 Introdution to Numerical Analysis (Berlin: Springer)
13. 1-Lohner algorithm Found. Comput. Math. 2 429-65