Blow up of the isosceles 3--body problem with an infinitesimal mass
Martha Alvarez-Ramírez - Departamento de Matemáticas, Universidad Autónoma Metropolitana – Iztapalapa, A. P. 55-534, 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  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 . 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  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; Published: June 2003.
2011 Impact Factor.913