Blow up of the isosceles 3body problem with an infinitesimal mass
Martha AlvarezRamírez  Departamento de Matemáticas, Universidad Autónoma Metropolitana – Iztapalapa, A. P. 55534, 09340 Iztapalapa, México, D. F., Mexico (email) Abstract: We consider the isosceles $3$body problem with the third particle having a small mass which eventually tend to zero. Classical McGehee's blow up is not defined because the matrix of masses becomes degenerate. Following Elbialy [3] we perform the blow up using the Euclidean norm in the planar $3$body problem. We then complete the phase portrait of the flow in the collision manifold giving the behavior of some branches of saddle points missing in [3]. The homothetic orbits within the fixed energy level then provide the necessary recurrence in order to build a symbolic dynamics. This is done following ideas of S. Kaplan [6] for the collinear $3$body problem. Here the difficulty is the larger number of critical points.
Keywords: 3–body problem, blow up, restricted isosceles problem, symbolic dynamics.
Received: May 2002; Revised: December 2002; Available Online: June 2003. 
2014 IF (1 year).972
