Planar central configurations can be seen as critical points of the reduced potential or solutions of a system of equations. By the homogeneity of the potential and its O(2)-invariance it is possible to see that the SO(2)- orbits of central configurations are fixed points of a map f. The purpose of the paper is to define and study this map and to derive some properties using topological fixed point theory. The generalized Moulton-Smale theorem for collinear configurations is proved, together with some estimates on the number of central configurations in the case of three bodies, using fixed point indices. Well-known results such as the compactness of the set of central configurations follow easily in this topological framework. © 2007 Birkhaeuser.

Ferrario, D. (2007). Planar central configurations as fixed points. JOURNAL OF FIXED POINT THEORY AND ITS APPLICATIONS, 2(2), 277-291 [10.1007/s11784-007-0032-7].

Planar central configurations as fixed points

FERRARIO, DAVIDE LUIGI
2007

Abstract

Planar central configurations can be seen as critical points of the reduced potential or solutions of a system of equations. By the homogeneity of the potential and its O(2)-invariance it is possible to see that the SO(2)- orbits of central configurations are fixed points of a map f. The purpose of the paper is to define and study this map and to derive some properties using topological fixed point theory. The generalized Moulton-Smale theorem for collinear configurations is proved, together with some estimates on the number of central configurations in the case of three bodies, using fixed point indices. Well-known results such as the compactness of the set of central configurations follow easily in this topological framework. © 2007 Birkhaeuser.
Articolo in rivista - Articolo scientifico
central configurations; fixed points
English
2007
2
2
277
291
none
Ferrario, D. (2007). Planar central configurations as fixed points. JOURNAL OF FIXED POINT THEORY AND ITS APPLICATIONS, 2(2), 277-291 [10.1007/s11784-007-0032-7].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/774
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