Complete classification of homoclinic cycles in ℝ4 in the case of symmetry group G ⊂ SO(4);Classification complète des cycles homoclines de ℝ4 dans le cas d'un groupe de symétrie G ⊂ SO(4)

Comptes Rendus Mathematique

Volumn 334, Issue 10, 2002, Pages 859-864

  Sottocornola, Nicola ^a  

^a INSTITUT NON LINÉAIRE DE NICE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038391468     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1631-073X(02)02371-3     Document Type: Article

References (11)

1. P. Ashwin, J. Montaldi, Conditions for existence of robust relative homoclinic trajectories, Math. Proc. Cambridge Philos. Soc., 2002, to appear.
2. P. Chossat, M. Krupa, I. Melbourne, A. Scheel, Transverse bifurcation of homoclinic cycles, Phys. D 100 (1997) 85-100.
3. P. Chossat, R. Lauterbach, Methods in Equivariant Bifurcation and Dynamical Systems, Adv. Ser. Nonlinear Dynam., Vol. 15, World Scientific, 2000.
4. P. Du Val, Homographies Quaternions and Rotations, Oxford University Press, 1964.
5. J. Guckenheimer, P. Holmes, Structurally stable heteroclinic cycles, Math. Proc. Cambridge Philos. Soc. 103 (1988) 189-192.
6. M. Krupa, Robust heteroclinic cycles, J. Nonlinear Sci. 7 (1997) 129-176.
7. M. Krupa, I. Melbourne, Asymptotic stability of heteroclinic cycles in systems with symmetry, Ergodic Theory Dynamical Systems 15 (1) (1995) 121-147.
8. G. Myerson, Rational products of sines of rational angles, Aequationes Math. 45 (1993) 70-82.
9. M. Newman, Some results on roots of unity, with an application to a diophantine problem, Aequationes Math. 2 (1969) 163-166.
10. N. Sottocornola, Sur la classification des cycles homoclines, C. R. Acad. Sci. Paris, Serie I 332 (2001) 695-698.
11. 4, Nonlinearity, submitted.