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A characterization of the Ligon-Schaaf regularization map

✍ Scribed by R. H. Cushman; J. J. Duistermaat

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 124 KB
Volume: 50
Category: Article
ISSN: 0010-3640
DOI: 10.1002/(sici)1097-0312(199708)50:8<773::aid-cpa3>3.0.co;2-3

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✦ Synopsis

First, we give an explicit description of all the mappings from the phase space of the Kepler problem to the phase space of the geodesics on the sphere, which transform the constants of motion of the Kepler problem to the angular momentum. Second, among these we describe those mappings that in addition send Kepler solutions to parametrized geodesics. Third, we describe those mappings that in addition are canonical transformations of the respective phase space. Finally, we prove that among these, the Ligon-Schaaf map is the unique one which maps the collision orbits to the geodesics that pass through the north pole. In this way we also give a new proof that the Ligon-Schaaf map has all the properties described above.

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