Types of escapes in a simple Hamiltonian system

Details Types of escapes in a simple Hamiltonian system Types of escapes in a simple Hamiltonian system

Jan 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992a%26a...253..379c&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 253, no. 2, Jan. 1992, p. 379-388. Research supported by NSF.

Astronomy and Astrophysics

Astrophysics

14

Hamiltonian Functions, Kinematics, Orbital Mechanics, Stellar Motions, Asymptotic Methods, Liapunov Functions

Scientific paper

The proportion of escaping orbits in a Hamiltonian system and the direction of escape depend on the topology of the asymptotic surfaces of the Liapunov periodic orbits (i.e., orbits at the throats of the various escape channels). This paper investigates the topology of these asymptotic surfaces in a Hamiltonian which has four escape channels. The 'basins' of escape toward different directions, and of the fast and the slow escapes for various values of the perturbation parameter (epsilon) are determined. It is found that, as the epsilon values decrease and approach the value for escape perturbation (epsilon(esc)), the proportion R of fast escapers decreases. An equation expressing the mathematical relationship between R and the difference of perturbations epsilon - epsilon(esc) is determined.

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