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Title: Arnold diffusion in the elliptic Hill four-body problem: geometric method and numerical verification
We present a mechanism for Arnold diffusion in energy in a model of the elliptic Hill four-body problem. Our model is expressed as a small perturbation of the circular Hill four-body problem, with the small parameter being the eccentricity of the orbits of the primaries. The mechanism relies on the existence of two normally hyperbolic invariant manifolds (NHIM's), and on the corresponding homoclinic and heteroclinic connections. The dynamics along homoclinic/heteroclinic orbits is encoded via scattering maps, which we compute numerically. Having several scattering maps, at each point we select the scattering map that gives the largest gain in energy or the scattering map that gives the smallest loss in energy. Using Birkhoff's Ergodic Theorem we show that there are pseudo-orbits generated by the selected scattering maps along which, on average, the energy grows by an amount independent of the small parameter. A shadowing lemma yields the existence of diffusing orbits.  more » « less
Award ID(s):
2307718
PAR ID:
10519250
Author(s) / Creator(s):
; ;
Publisher / Repository:
IOP
Date Published:
Journal Name:
Nonlinearity
ISSN:
2573-1793
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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