Asymptotic curves and escapes in Hamiltonian systems

Details Asymptotic curves and escapes in Hamiltonian systems Asymptotic curves and escapes in Hamiltonian systems

May 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990a%26a...231...41c&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 231, no. 1, May 1990, p. 41-55.

Astronomy and Astrophysics

Astrophysics

21

Asymptotic Methods, Escape Velocity, Hamiltonian Functions, Stellar Orbits, Stellar Systems, Celestial Mechanics, Liapunov Functions, Orbital Elements

Scientific paper

Escapes in two Hamiltonian systems that may represent the central parts of perturbed galaxies are explored. One case has quadruple symmetry and four openings to infinity, while the second has only one axis of symmetry and two openings. Every opening is bridged by an unstable periodic orbit called a Lyapunov orbit. Any orbit that crosses a Lyapunov orbit outward escapes to infinity. The asymptotic curves of the various Lyapunov orbits form many oscillations and then make infinite rotations around some 'limiting curves'. In the first model there are four Lyapunov orbits whose characteristics intersect at infinite homoclinic and heteroclinic points that define intervals of escape. In the second model there are only two Lyapunov orbits. Limiting curves in the forward and backward directions and the initial conditions leading to those curves are found.

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