Preprint A291/2004
Topological Classification of Multiple Saddle Connections

Felipe Cano | Alonso-González, Clementa | Camacho, M. Izabel

**Keywords: **
dynamical systems | topological classification | saddle-connections | blowing-up

In this paper we deal with real analytic vector fields in an
ambient space of dimension three. The existence of em
connections of hyperbolic saddles along the skeleton of the
exceptional divisor is one of the major problems in order to get
topological equivalences by means of a desingularization morphism.
We give a complete topological classification of such multiple
saddle connections under the assumption that the graph of
connections has no cycles. For a given divisor and skeleton, the
classifying space has a geometrical description, is finite and
depends only on the distribution of the eigenvalues. We use in an
essential way the control of the inverse propagation of a
homeomorphism defined in a transversal disc of the one dimensional
invariant variety to get a whole topological equivalence between
two saddles.