Fractal Basins In Hénon-heiles And Other Polynomial Potentials

Abstract

The dynamics of several Hamiltonian systems of two degrees of freedom with polynomial potentials is examined. All these systems present unbounded trajectories escaping along different routes. The motion in these open systems is characterized by a fractal boundary (and its corresponding fractal dimension) separating the basins of the escape routes. The fractal (basin boundary) dimensions for these systems are studied in some detail. © 1999 Elsevier Science B.V. All rights reserved.2565-6362368Contopoulos, G., (1990) Astron. Astrophys., 231, p. 41Contopoulos, G., Kaufmann, D., (1992) Astron. Astrophys., 253, p. 379Contopoulos, G., Polymilis, C., (1993) Phys. Rev. E, 46, p. 1546Contopoulos, G., Kandrup, H.E., Kaufmann, D., (1993) Phys. D, 64, p. 310Podolský, J., Veselý, K., (1998) Phys. Rev. D, 58. , 081501, gr-qc 9805078Podolský, J., Veselý, K., Chaotic Motion in pp-wave Spacetimes, , Preprint: gr-qc 9809065Ott, E., (1993) Chaos in Dynamical Systems, , Cambridge University Press, CambridgeHénon, M., Heiles, C., (1964) Astron. J., 69, p. 73Churchill, R.C., Pecelli, G., Rod, D.L., (1975) J. Diff. Equ., 17, p. 329Churchill, R.C., Rod, D.L., (1976) J. Diff. Equ., 21, p. 39(1976) J. Diff. Equ., 21, p. 66(1977) J. Diff. Equ., 24, p. 329Bleher, S., Grebogi, C., Ott, E., Brown, R., (1988) Phys. Rev. A, 38, p. 930Jánosi, I.M., Tél, T., Wolf, D.E., Gallas, J.A.C., (1997) Phys. Rev. E, 56, p. 285