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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.