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This article is cited in 3 scientific papers (total in 3 papers)
Alexey Borisov Memorial Volume
Darboux Inversions of the Kepler Problem
Alain Albouya, Lei Zhaob a IMCCE, UMR 8028,
77, avenue Denfert-Rochereau, F-75014 Paris, France
b Institute of Mathematics, University of Augsburg,
86135 Augsburg, Germany
Abstract:
While extending a famous problem asked and solved by Bertrand in 1873, Darboux found in 1877 a family of abstract surfaces of revolution, each endowed with a force function, with the striking property that all the orbits are periodic on open sets of the phase space. We give a description of this family which explains why they have this property: they are the Darboux inverses of the Kepler problem on constant curvature surfaces. What we call the Darboux inverse was briefly introduced by Darboux in 1889 as an alternative approach to the conformal maps that Goursat had just described.
Keywords:
conformal changes, periodic orbits, superintegrable systems.
Received: 18.12.2021 Accepted: 21.03.2022
Citation:
Alain Albouy, Lei Zhao, “Darboux Inversions of the Kepler Problem”, Regul. Chaotic Dyn., 27:3 (2022), 253–280
Linking options:
https://www.mathnet.ru/eng/rcd1164 https://www.mathnet.ru/eng/rcd/v27/i3/p253
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Abstract page: | 75 | References: | 24 |
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