Transition functions and moduli of stability for 3-dimensional homogeneous vector fields with a hyperbolic blowing-up (Q1181691)

The author introduces a method to calculate the transition function for saddle connections of planar diffeomorphisms by use of the ``normal transition function'', which is a positive multiple of the usual transition function given by W. de Melo and the author in J. Differ. Equations 75, No. 1, 88-102 (1988; Zbl 0672.58036), but it is defined directly without using \(C^ 1\)-linearizing coordinates. An advantage of this new presentation is the possibility to prove that the normal transition function is analytic if it is the case for the diffeomorphism. The second part of the paper deals with the existence of a modulus of stability for germs on \(R^ 3\) of homogeneous polynomial vector fields with a hyperbolic blowing-up.