On the Hénon and Heiles system in three dimensions: The role of the axial symmetry

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 228, Issue 4-5, 1997, Pages 255-260

  Ferrer, S ^a   Palacian J ^b   San Juan, J F ^c   Viartola, A ^a   Yanguas, P ^b  

^a UNIVERSITY OF ZARAGOZA   (Spain)

^b PUBLIC UNIVERSITY OF NAVARRE   (Spain)

^c UNIVERSITY OF LA RIOJA   (Spain)

Author keywords

Bifurcation; Normalization; Periodic orbit; Perturbed oscillator; Relative equilibria

Indexed keywords

BIFURCATION (MATHEMATICS);

AXIAL SYMMETRY; NORMALIZATION; PERIODIC ORBITS; PERTURBED OSCILLATORS; RELATIVE EQUILIBRIA; THREE DIMENSIONS;

CHAOS THEORY;

EID: 0000039278     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0375-9601(97)00110-2     Document Type: Article

References (25)

1. S. Ferrer and J. Gárate, New trends in Hamiltonian systems and celestial mechanics, eds. E. Lacomba and J. Llibre, ASND 8 (World Scientific, Singapore, 1996) p. 179.
2. S. Ferrer, M. Lara, J. Palacián and P. Yanguas, in Hamiltonian systems with three or more degrees of freedom, ed. A. Delshams (Kluwer, Dordrecht, 1996), to appear.
3. S. Ferrer, M. Lara, J. Palacián, A. Viartola, J.F. San Juan and P. Yanguas, Int. J. Bifurc. Chaos (1997), submitted.
4. S. Ferrer, M. Lara, J. Palacián, A. Viartola, J.F. San Juan and P. Yanguas, Int. J. Bifurc. Chaos (1997), submitted.
5. R. Cushman, S. Ferrer and H. Hanßmann (1997), in preparation.
6. M. Hénon and C. Heiles, Astron. J. 69, (1964) 73.
7. M.C. Gutzwiller, Chaos in classical and quantum mechanics, IAM 1 (Springer, Berlin, 1991).
8. A.J. Lichtenberg and M.A. Lieberman, Regular and chaotic dynamics, AMS 38 (Springer, Berlin, 1992).
9. K.T.R. Davies, T.E. Huston and M. Baranger, CHAOS 2 (1992) 215.
10. B.R. Miller, Celes. Mech. Dynam. Astron. 51 (1991) 251, and references therein.
11. R.C. Churchill, G. Pecelli and D.L. Rod, in: Stochastic behavior in classical and quantum Hamiltonian systems, eds. G. Casati and J. Ford, LNP 93 (Springer, Berlin, 1979) p. 76.
12. R.C. Churchill, M. Kummer and D.L. Rod, J. Diff. Equat. 49 (1983) 359.
13. D.M. Fradkin, Am. J. Phys. A 33 (1965) 207.
14. J. Moser, Comm. Pure Appl. Math. 23 (1970) 609.
15. J.A. Sanders and F. Verhulst, Averaging methods in nonlinear dynamical systems, AMS 59 (Springer, Berlin, 1985).
16. J.M. Arms, R. Cushman and J.M. Gotay, in: The geometry of Hamiltonian systems, ed. T. Ratiu (Springer, Berlin, 1991) p. 33.
17. H. Robe, Astron. Astrophys. 142 (1985) 351; 182 (1987) 202.
18. H. Robe, Astron. Astrophys. 142 (1985) 351; 182 (1987) 202.
19. F. Verhulst, Philos. Trans. R. Soc. A 290 (1979) 435.
20. T. de Zeeuw, Month. Not. R. Astron. Soc. 215 (1985) 731.
21. A. Deprit, Celes. Mech. 1 (1969) 12.
22. A. Deprit, Celes. Mech. Dynam. Astron. 51 (1991) 201.
23. S. Smale, Inv. Math. 10 (1970) 305.
24. P. Pascua, J.L. Rubio, A. Viartola and S. Ferrer, Int. J. Bifurc. Chaos 6 (1996) 1411.
25. P. Yanguas, Ph.D. thesis (1997), in preparation.