An equivariant, inclination-flip, heteroclinic bifurcation

Nonlinearity

Volumn 9, Issue 3, 1996, Pages 631-647

  Worfolk, P A ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041086027     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/9/3/002     Document Type: Article

References (18)

1. Arnold V I 1988 Geometrical Methods in the Theory of Ordinary Differential Equations (Berlin: Springer)
2. Brjuno A D 1971 Analytical form of differential equations Trans. Moscow Math. Soc. 25 131-288
3. Deng B 1993 Homoclinic twisting bifurcation and cusp horseshoe maps J. Dynam. Diff. Eq. 5 (3) 417-67
4. Devaney R L 1989 An Introduction to Chaotic Dynamical Systems Second edition (New York: Addison Wesley)
5. Field M 1977 Transversality in G-manifolds Trans. Am. Math. Soc. 231 429-50
6. Field M and Swift J 1991 Stationary bifurcation to limit cycles and heteroclinic cycles Nonlinearity 4 1001-43
7. Field M J 1989 Equivariant bifurcation theory and symmetry breaking J. Dynam. Diff. Eq. 1 (4) 369-421
8. Field M J and Richardson R W 1992 Symmetry-breaking and branching patterns in equivariant bifurcation theory, II. Arch. Rat. Mech. Anal. 120 147-190
9. Guckenheimer J and Holmes P 1988 Structurally stable heteroclinic cycles Math. Proc. Camb. Phil. Soc. 103 189-192
10. Guckenheimer J and Holmes P J 1983 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (New York: Springer)
11. Guckenheimer J and Worfolk P 1992 Instant chaos Nonlinearity 5 1211-22
12. Guckenheimer J and Worfolk P 1993 Dynamical systems: Some computational problems Bifurcations and Periodic Orbits of Vector Fields ed D Schlomiuk (NATO ASI Series C: Mathematical and Physical Sciences) (Dordrecht: Kluwer)
13. Hénon M 1976 A two-dimensional mapping with a strange attractor Commun. Math. Phys. 50 69-77
14. Homburg A J, Kokubu H and Krupa M 1994 The cusp horseshoe and its bifurcations in the unfolding of am inclination-flip homoclinic orbit Ergod. Theor. Dynam. Syst. 14 (4) 667-693
15. Robinson C 1989 Homoclinic bifurcation to a transitive attractor of Lorenz type Nonlinearity 2 495-518
16. Robinson C 1992 Homoclinic bifurcation to a transitive attractor of Lorenz type, II SIAM J. Math. Anal. 23(5) 1255-1268
17. Rychlik M 1989 Lorenz attractors through šilnikov-type bifurcation - Part I Ergod. Theor. Dynam. Syst. 10 793-821
18. Siegel C L 1952 Über die Normalform analytischer Differentialgleichungen in der Nähe einer Gleichgewichtslösung. Nachr. Akad. Wiss. Göttingen 21-30