Journal
CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY
Volume 79, Issue 4, Pages 297-314Publisher
KLUWER ACADEMIC PUBL
DOI: 10.1023/A:1017536931038
Keywords
chaotic scattering; Poincare section; coorbital satellites; Hill's problem
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The fractal nature of the transitions between two sets of orbits separated by heteroclinic or homoclinic orbits is well known. We analyze in detail this phenomenon in Hill's problem where one set of orbits corresponds to coorbital satellites exchanging semi-major axis after close encounter (horse-shoe orbits) and the other corresponds to orbits which do not exchange semi-major axis (passing-by orbits). With the help of a normalized approximation of the vicinity of unstable periodic orbits, we show that the fractal structure is intimately tied to a special spiral structure of the Poincare maps. We show that each basin is composed of a few 'well behaved' areas and of an infinity of intertwined tongues and subtongues winding around them. This behaviour is generic and is likely to be present in large classes of chaotic scattering problems.
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