Topological Classification of Multiple Saddle Connections
Felipe Cano | Alonso-González, Clementa | Camacho, M. Izabel
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.