TY - JOUR
T1 - Stability diagram for 4D linear periodic systems with applications to homographic solutions
AU - Martínez, Regina
AU - Samà, Anna
AU - Simó, Carles
PY - 2006/7/15
Y1 - 2006/7/15
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/33645080970
U2 - 10.1016/j.jde.2006.01.014
DO - 10.1016/j.jde.2006.01.014
M3 - Article
SN - 0022-0396
VL - 226
SP - 619
EP - 651
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -