Vanishing twist near focus-focus points

Nonlinearity

Volumn 17, Issue 5, 2004, Pages 1777-1785

  Dullin, Holger R ^a,c   San, Vũ Ngoc ^b  

^a UNIVERSITY OF BREMEN   (Germany)

^b INSTITUT FOURIER   (France)

^c LOUGHBOROUGH UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4644273775     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/17/5/012     Document Type: Article

References (29)

1. Arnold V I 1978 Mathematical Methods of Classical Mechanics (Berlin: Springer)
2. Birkhoff G D 1927 Dynamical Systems (Providence, RI: American Mathematical Society)
3. Cushman R H and Bates L M 1997 Global Aspects of Classical Integrable Systems (Basel: Birkhäuser)
4. del Castillo-Negrette D, Greene J M and Morrison P J 1996 Area preserving nontwist maps: periodic orbits and transition to chaos Physica D 91 1-23
5. Duistermaat J J 1980 On global action-angle coordinates Commun. Pure Appl. Math. 33 687-706
6. Duistermaat J J 1998 The monodromy in the Hamiltonian Hopf bifurcation Z. Angew. Math. Phys. 49 156-61
7. Dullin H R and Ivanov A V 2004 Vanishing twist in the Hamiltonian Hopf bifurcation Physica D under consideration
8. Dullin H R, Meiss J D and Sterling D G 2000 Generic twistless bifurcations Nonlinearity 13 203-24
9. Eliasson L H1984 Hamiltonian systems with Poisson commuting integrals PhD Thesis University of Stockholm
10. Horozov E 1990 Perturbations of the spherical pendulum and Abelian integrals J. Reine Angew. Math. 408 114-35
11. Horozov E 1993 On the isoenergetical nondegeneracy of the spherical pendulum Phys. Lett. A 173 279-83
12. Howard J E and Hohs S M 1984 Stochasticity and reconnection in Hamiltonian systems Phys. Rev. A 29 418
13. Ito H 1989 Convergence of Birkhoff normal forms for integrable systems Comment. Math. Helv. 64 412-61
14. Ito H 1991 Action-Angle coordinates at singularities for analytic integrable systems Math. Z. 206 363-407
15. Knörrer H 1985 Singular fibres of the momentum mapping for integrable Hamiltonian systems J. Reine Angew. Math. 355 67-107
16. Matveev V S 1996 Integrable Hamiltonian systems with two degrees of freedom. Topological structure of saturated neighborhoods of saddle-saddle and focus-focus types Matem. Sbornik 187 29-58
17. Meyer K R and Hall G R1992 Introduction to Hamiltonian Dynamical Systems and the N-Body Problem (Berlin: Springer)
18. Rink B 2004 A Cantor set of tori with monodromy near a focus-focus singularity Nonlinearity 17 347-56
19. Rüssmann H 1964 Über das Verhalten analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung Math. Ann. 154 285-300
20. Rüssmann H 1989 Nondegeneracy in the perturbation theory of integrable dynamical systems Number Theory and Dynamical Systems (York, 1987) (London Mathematical Society Lecture Note Series vol 134)(Cambridge: Cambridge University Press) pp 5-18
21. Siegel C L and Moser J K 1971 Lectures on Celestial Mechanics (Heidelberg: Springer)
22. Simó C 1998 Invariant curves of analytic perturbed nontwist area preserving maps Regular and Chaotic Dynamics 3 180-95
23. van der Meer J-C 1985 The Hamiltonian Hopf Bifurcation (Lecture Notes in Mathematics vol 1160) (Berlin: Springer)
24. Vey J 1978 Sur certains systèmes dynamiques séparables Am. J. Math. 100 591-614
25. Vu Ngõc S 2000 Bohr-Sommerfeld conditions for integrable systems with critical manifolds of focus-focus type Comm. Pure Appl. Math. 53 143-217
26. Vu Ngõc S 2003 On semi-global invariants for focus-focus singularities Topology 42 365-80
27. Williamson J 1936 On the algebraic problem concerning the normal forms of linear dynamical systems Am. J. Math. 58 141-63
28. Zung N T 1996 Kolmogorov condition for integrable systems with focus-focus singularities Phys. Lett. A 215 40-4
29. Zung N T 1997 A note on focus-focus singularities Diff. Geom. Appl. 7 123-30