Zastosowanie metod niezmienniczej analizy nieliniowej do badania istnienia i bifurkacji centralnych konfiguracji pewnych zagadnień mechaniki nieba

Abstract

We study topological bifurcations of critical orbits of equivariant gradient equations. We give necessary and sufficient conditions for the existence of global bifurcations of solutions of these equations. Moreover, we apply these abstract results to the study of bifurcations of new families of planar and spatial central configurations of the N-body problem. It is worth pointing out that the shapes of the bifurcating families are less symmetrical than the shapes of the considered families of planar and spatial central configurations.