Resonances for weak coupling of the unfolding of a saddle-node periodic orbit with an oscillator

Nonlinearity

Volumn 20, Issue 5, 2007, Pages 1283-1298

  Baesens, C ^a   MacKay, R S ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34249309927     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/20/5/012     Document Type: Article

References (19)

1. Afraimovich V S and Young T 2000 Mather invariants and smooth conjugacy on J. Dyn. Control Sys. 6 341-52
2. Asimov D and Franks J 1983 Unremovable closed orbits Geometric dynamics (Lecture Notes in Maths vol 1007) ed J Palis (Berlin: Springer) pp 22-9
3. Baesens C, Guckenheimer J, Kim S and MacKay R S 1991 Three coupled oscillators: mode-locking, global bifurcations and toroidal chaos Physica D 49 387-475
4. Baesens C, Guckenheimer J, Kim S and MacKay R S 1991 Simple resonance regions of torus diffeomorphisms Patterns and Dynamics in Reactive Media Proc. IMA (Minneapolis, 1989) (IMA Vol. in Maths and its Applications) vol 37 ed R Aris et al (Berlin: Springer) pp 1-9
5. Broer H W, Naudot V, Roussarie R, Saleh K and Wagener F O O 2007 Organising centres in the semi-global analysis of dynamical systems Int. J. Appl. Math. Stat. in press
6. Chenciner A 1988 Bifurcations de points fixes elliptiques: III. Orbites périodiques de ≪petites≫ périodes et élimination résonnante des couples de courbes invariantes Publ. Math. IHES 66 5-91
7. Chenciner A, Gasull A and Llibre J 1987 Une description complète du portrait de phase d'un modèle d'élimination résonante C. R. Acad. Sci. Paris Sér I 305 623-6
8. Conley C 1988 The gradient structure of a flow: I Ergod. Theory Dynam. Syst. 8 11-26
9. Dumortier F, Roussarie R and Sotomayor J 1987 Generic three parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part: the cusp case of codimension 3 Ergod. Theory Dynam. Syst. 7 375-413
10. Fried D 1982 Flow equivalence, hyperbolic systems and a new zeta function for flows Commun. Math. Helv. 57 237-59
11. Guckenheimer J and Holmes P J 1990 Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields 2nd edn (Berlin: Springer)
12. Handel M 1985 Global shadowing of pseudo-Anosov homeomorphisms Ergod. Theory Dynam. Syst. 5 373-7
13. Il'yashenko Yu S and Yakovenko S Yu 1993 Nonlinear Stokes phenomena in smooth classification problems Adv. Sov. Math. 14 235-87 Nonlinear Stokes Phenomenon ed Yu S Ilyashenko
14. Il'yashenko Yu S and Yakovenko S Yu 1991 Finitely-smooth normal forms of local families of diffeomorphisms and vector fields Russ. Math. Surv. 46 1-43
15. Levi M 1988 Nonchaotic behavior in the Josephson junction Phys. Rev. A 37 927-31
16. Lochak P and Meunier C 1988 Multiphase Averaging for Classical Systems (Berlin: Springer)
17. Sanders J A and Verhulst F 1985 Averaging Methods in Nonlinear Dynamical Systems (Berlin: Springer)
18. Takens F and Wagener F O O 2000 Resonances in skew and reducible quasi-periodic Hopf bifurcation Nonlinearity 13 377-96
19. Yoccoz J-C 1987 Bifurcation de points fixes élliptiques (d'après A Chenciner) Asterique 145-146 313-34 Séminaire Bourbaki no 668 in