The threshold of chaos for Henon-Heiles and related potentials

Details The threshold of chaos for Henon-Heiles and related potentials The threshold of chaos for Henon-Heiles and related potentials

Nov 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985aj.....90.2377i&link_type=abstract

Astronomical Journal (ISSN 0004-6256), vol. 90, Nov. 1985, p. 2377-2380. NSERC-supported research.

Astronomy and Astrophysics

Astronomy

9

Chaos, Particle Motion, Potential Theory, Differential Equations, Disk Galaxies, Equations Of Motion, Harmonic Oscillators, Schroedinger Equation

Scientific paper

It is shown that a crucial part of the orbit of a particle released from rest in Hénon-Heiles and related potentials near the chaotic threshold is accurately described by an equation formally similar to the Schrödinger equation for the harmonic oscillator. Its solution in this neighborhood yields an improved physical understanding of the interplay between the various terms in this type of potential, which can lead to an abrupt transition from ordered to chaotic motion for some energies. It is also thereby possible to understand physically how ordered motion may reappear for limited higher-energy regimes.

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