Planar radial weakly dissipative diffeomorphisms

Chaos

Volumn 20, Issue 4, 2010, Pages

  Simo C ^a   Vieiro, A ^a  

^a UNIVERSITY OF BARCELONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78650695947     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3515168     Document Type: Article

References (30)

1. Arnold V.I. Chapitres Supplémentaires de la Théorie des Équations Différentielles Ordinaires 1978, (Mir, Moscow).
2. Arrowsmith D.K. Place C.M. An Introduction to Dynamical Systems 1990, and (Cambridge University Press, Cambridge).
3. Broer H. Roussarie R. Simó C. Invariant circles in the Bogdanov-Takens bifurcation for diffeomorphisms. Ergod. Theory Dyn. Syst. 1996, 16:1147-1142. ZZZZZZ, 0143-3857, 10.1017/S0143385700009950.
4. Broer H. Simó C. Tatjer J.C. Towards global models near homoclinic tangencies of dissipative diffeomorphisms. Nonlinearity 1998, 11:667-770. NONLE5, 0951-7715, 10.1088/0951-7715/11/3/015.
5. Celletti A. Weakly dissipative systems in celestial mechanics. Lecture Notes in Physics 2007, 729:67. 10.1007/978-3-540-72984-6_3.
6. del Castillo-Negrete D. Greene J.M. Morrison P.J. Area preserving nontwist maps: Periodic orbits and transition to chaos. Physica D 1996, 91:1-23. PDNPDT, 0167-2789, 10.1016/0167-2789(95)00257-X.
7. del Castillo-Negrete D. Morrison P.J. Chaotic transport by Rossby waves in shear flow. Phys. Fluids A 1993, 5:948-965. PFADEB, 0899-8213, 10.1063/1.858639.
8. Dullin H.R. Meiss J.D. Sterling D. Generic twistless bifurcations. Nonlinearity 1999, 13:203-224. NONLE5, 0951-7715, 10.1088/0951-7715/13/1/310.
9. 1 in the Earth-Sun system. Celest. Mech. Dyn. Astron. 2010, 107:233-253. CMDAEP, 0923-2958, 10.1007/s10569-010-9268-4.
10. Fontich E. Simó C. The splitting of separatrices for analytic diffeomorphism. Ergod. Theory Dyn. Syst. 1990, 10:295-318. ZZZZZZ, 0143-3857.
11. Guckenheimer J. Holmes P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields 1997, 42. and Applied Natural Sciences, Vol. (Springer, New York).
12. Hénon M. Numerical study of quadratic area-preserving mappings. Q. Appl. Math. 1969, 27:291-312. QAMAAY, 0033-569X.
13. Hénon M. A two dimensional mapping with a strange attractor. Commun. Math. Phys. 1976, 50:69-77. CMPHAY, 0010-3616, 10.1007/BF01608556.
14. Holmes P. Whitley D. Bifurcations of one- and two-dimensional maps. Philos. Trans. R. Soc. London, Ser. A 1984, 311:43-102. PTRMAD, 0962-8428, 10.1098/rsta.1984.0020.
15. McLaughlin J. Stochastic behavior in slightly dissipative systems. Phys. Rev. A 1979, 20:2114-2119. PLRAAN, 1050-2947, 10.1103/PhysRevA.20.2114.
16. Neishtadt A.I. On probabilistic phenomena in perturbed systems. Sel. Math. Sov. 1993, 12:195-210. SMSODB, 0272-9903.
17. Neishtadt A.I. On averaging in two-frequency systems with small Hamiltonian and much smaller non-Hamiltonian perturbations. Mosc. Math. J. 2003, 3:1039-1052. ZZZZZZ, 1609-3321.
18. Piftankin G.N. Treschev D.V. Separatrix maps in Hamiltonian systems. Russ. Math. Surveys 2007, 2:219-322. RMSUAF, 0036-0279, 10.1070/RM2007v062n02ABEH004396.
19. Rabassa P. Contribution to the study of perturbations of low dimensional maps. 2010, Ph.D. thesis, Universitat de Barcelona.
20. Samelson R.M. Fluid exchange across a meandering jet. J. Phys. Oceanogr. 1992, 22:431-444. JPYOBT, 1520-0485, 10.1175/1520-0485(1992)022<0431:FEAAMJ>2.0.CO;2.
21. Siegel C.L. Moser J.K. Lectures on Celestial Mechanics 1971, Berlin. and (Springer-Verlag).
22. Simó C. Invariant curves of analytic perturbed nontwist area preserving maps. Regular Chaotic Dyn. 1998, 3:180-195. ZZZZZZ, 10.1070/rd1998v003n03ABEH000088.
23. Simó C. Stuchi T. Central stable/unstable manifolds and the destruction of KAM tori in the planar Hill problem. Physica D 2000, 140:1-32. PDNPDT, 0167-2789, 10.1016/S0167-2789(99)00211-0.
24. Simó C. Vieiro A. A numerical exploration of weakly dissipative two-dimensional maps. 2005, and Proceedings of ENOC'05.
25. Simó C. Vieiro A. Resonant zones, inner and outer splittings in generic and low order resonances of area preserving maps. Nonlinearity 2009, 22:1191-1245. NONLE5, 0951-7715, 10.1088/0951-7715/22/5/012.
26. Simó C. Vieiro A. Dynamics in chaotic zones of area preserving maps: close to separatrix and global instability zones. Physica D PDNPDT, 0167-2789, and (submitted).
27. Simó C. Vieiro A. Dynamical description of the domain of stability of area preserving maps. and (unpublished).
28. Simó C. Vieiro A. Planar radial weakly-dissipative diffeomorphisms: Homoclinic-type resonances. and (unpublished).
29. Takens F. Forced oscillations and bifurcations. Applications of Global Analysis, I 1974, 1-59. (Math. Inst. Rijksuniv., Utrecht), pp.
30. Wolansky G. Limit theorem for a dynamical system in the presence of resonances and homoclinic orbits. J. Differ. Equations 1990, 83:300-335. JDEQAK, 0022-0396, 10.1016/0022-0396(90)90060-3.