Non-Integrability of the Generalized Two Fixed Centres Problem |
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| Authors: | Andrzej J. Maciejewski Maria Przybylska |
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| Affiliation: | (1) Institute of Astronomy, University of Zielona Góra, Podgórna 50, PL-65-246 Zielona Góra, Poland;(2) INRIA Projet CAFé 2004, Route des Lucioles, B.P. 93, 06902 Sophia Antipolis Cedex, France;(3) Toruń Centre for Astronomy, Nicholaus Copernicus University, Gagarina 11, PL-87-100 Toruń, Poland |
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| Abstract: | We consider two fixed centres attracting a third body. Each centre is the source of a force field with potential V=−ar −2n , where n is a real number. We prove that this generalization of the classical two fixed centres problem is non-integrable except when n= 0, 1/2, −1 and −2. This revised version was published online in July 2006 with corrections to the Cover Date. |
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| Keywords: | integrability two fixed centres problem |
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