Global bifurcations from the center of mass in the Sitnikov problem

Pages: 719 - 732, Volume 14, Issue 2, September 2010

doi:10.3934/dcdsb.2010.14.719       Abstract        Full Text (210.0K)       Related Articles

Rafael Ortega - Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain (email)
Andrés Rivera - Departamento de Ciencias Naturales y Matemáticas, Facultad de Ingeniería, Pontificia Universidad Javeriana Cali, 26239 Cali, Colombia (email)

Abstract: The Sitnikov problem is a restricted three body problem where the eccentricity of the primaries acts as a parameter. We find families of symmetric periodic solutions bifurcating from the equilibrium at the center of mass. These families admit a global continuation up to excentricity $e=1$. The same techniques are applicable to the families obtained by continuation from the circular problem ($e=0$). They lead to a refinement of a result obtained by J. Llibre and R. Ortega.

Keywords:  3-body problem, Sitnikov problem, periodic orbits,bifurcations, global continuation.
Mathematics Subject Classification:  Primary: 70F07; Secondary: 34B15, 37G15, 37N05.

Received: June 2009;      Revised: November 2009;      Published: June 2010.