Shil'nikov configurations in any generic unfolding of the nilpotent singularity of codimension three on ℝ3

Journal of Differential Equations

Volumn 208, Issue 1 SPEC.ISS., 2005, Pages 147-175

  Iban S ^a   Rodriguez J A ^a  

^a UNIVERSITY OF OVIEDO   (Spain)

Author keywords

Heteroclinic cycles; Shil'nikov homoclinic orbits; Unfoldings of singularities

Indexed keywords

EID: 10944272553     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jde.2003.08.006     Document Type: Article

References (16)

1. Arneodo A. Coullet P. Spiegel E. Tresser C. Asymptotic chaos Physica D 14 1985 327-347
2. Dumortier F. Ibáñez S. Nilpotent singularities in generic 4-parameter families of 3-dimensional vector fields J. Differential Equations 127 1996 590-647
3. Dumortier F. Ibáñez S. Kokubu H. New aspects in the unfolding of the nilpotent singularity of codimension three Dynamical Systems 16 1 2001 63-95
4. F. Fernández-Sánchez, Comportamiento dinámico y de bifurcaciones en algunas conexiones globales de equilibrio en sistemas tridimensionales, Ph.D. Thesis, University of Sevilla, 2002.
5. Homburg A.J. Periodic attractors, strange attractors and hyperbolic dynamics near homoclinic orbit to saddle-focus equilibria Nonlinearity 15 2002 1029-1050
6. Ibáñez S. Rodríguez J.A. Sil'nikov bifurcations in generic 4-unfoldings of a codimension-4 singularity J. Differential Equations 120 1995 411-428
7. Ishimura N. Remarks on third-order ODEs relevant to the Kuramoto-Shivashinsky equation J. Differential Equations 178 2002 466-477
8. Kuramoto Y. Tsuzuki T. Persistent propagation of concentration waves in dissipative media far from thermal equilibrium Progr. Theoret. Phys. 55 1976 356-369
9. Lau Y.-T. The "cocoon" bifurcations in three-dimensional systems with two fixed points Internat. J. Bifur. Chaos Appl. Sci. Eng. 2 1992 543-558
10. Michelson D. Steady solutions of the Kuramoto-Sivashinsky equation Physica D 19 1986 89-111
11. Mora L. Viana M. Abundance of strange attractors Acta Math. 171 1993 1-71
12. Pumariño A. Rodŕguez J.A. Coexistence and persistence of strange attractors in: Lecture Notes in Mathematics Vol. 1658 1997 Springer Berlin
13. Pumariño A. Rodríguez J.A. Coexistence and persistence of infinitely many strange attractors Ergodic Theory Dyn. Systems 21 2001 1511-1523
14. Shil'nikov L.P. A case of the existence of a denumerable set of periodic motions Soviet Math. Dokl. 6 1965 163-166
15. C. Tresser, Modèles simples de transitions vers la turbulence, These d'Etat, Université de Nice, 1981.
16. Troy W.C. The existence of steady solutions of the Kuramoto Sivashinsky equation J. Differential Equations 82 1989 269-313