We consider a family of 4-dimensional Hamiltonian time-periodic linear systems depending on three parameters, λ1, λ2 and ε such that for ε = 0 the system becomes autonomous. Using normal form techniques we study stability and bifurcations for ε > 0 small enough. We pay special attention to the d'Alembert case. The results are applied to the study of the linear stability of homographic solutions of the planar three-body problem, for some homogeneous potential of degree -α, 0 < α < 2, including the Newtonian case. © 2006 Elsevier Inc. All rights reserved.
|Journal||Journal of Differential Equations|
|Publication status||Published - 15 Jul 2006|