Instability and Diffusion in the Elliptic Restricted Three-body Problem |
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Authors: | Xinhao Liao Donald G Saari |
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Institution: | (1) Shanghai Observatory, The Chinese Academy of Sciences, Shanghai, 200030, China;(2) Department of Mathematics, Northwestern University, Evanston, IL, 60208-2730, U.S.A |
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Abstract: | The importance of the stability characteristics of the planar elliptic restricted three-body problem is that they offer insight
about the general dynamical mechanisms causing instability in celestial mechanics. To analyze these concerns, elliptic–elliptic
and hyperbolic–elliptic resonance orbits (periodic solutions with lower period) are numerically discovered by use of Newton's
differential correction method. We find indications of stability for the elliptic–elliptic resonance orbits because slightly
perturbed orbits define a corresponding two-dimensional invariant manifold on the Poincaré surface-section. For the resonance
orbit of the hyperbolic–elliptic type, we show numerically that its stable and unstable manifolds intersect transversally
in phase-space to induce instability. Then, we find indications that there are orbits which jump from one resonance zone to
the next before escaping to infinity. This phenomenon is related to the so-called Arnold diffusion.
This revised version was published online in August 2006 with corrections to the Cover Date. |
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Keywords: | resonant orbit transversal intersection resonant jump diffusion instability |
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