TITLE: Asymptotic behaviour of the stability parameter for a family of singular-limit Hill's equation.

AUTHORS: 
R. Martinez
Dept. de Matematiques, Univ. Autonoma de Barcelona
Barcelona, Catalunya, Spain 
E-mail:reginamb@mat.uab.cat

A. Sama
Dept. de Matematiques, Univ. Autonoma de Barcelona
Barcelona, Catalunya, Spain
E-mail:sama@mat.uab.cat

ABSTRACT:
Under some non degeneracy conditions we give asymptotic formulae for the stability 
parameter of a family of singular-limit Hill's equation which depends on three 
parameters. We use the blow up techniques. The main contribution of this paper 
concerns the study of the non degeneracy conditions. We give a geometrical
interpretation of them, in terms of heteroclinic orbits for some related 
systems. In this way one can determine values of the parameters such that the
non degeneracy conditions are satisfied. As a motivation and application
we consider the vertical stability of homographic solutions in the three-body 
problem.

Preprint submitted to J. Differential Equations, 21 December 2007

Published in J. Differential Equations, 245 (2008) 3869-3897