Topological equivalence for multiple saddle connections
by
Clementa Alonso González
Universidad de Valladolid
Coauthors: M.I.T. Camacho, F. Cano

We proof the existence of a topological equivalence between two vector fields in the neighborhood of the skeleton of an invariant normal crossing divisor in a space of dimension three (the skeleton: union of intersections of pairs of divisors). The singularities are hyperbolic without certain algebraic resonances in the sets of eigenvalues and these sets are ``ordered in the same way". The main difficulty is to deal with the multiple saddle-connections in dimension three that appear. Once we cut-out the attractors, we get the result if the corresponding graph has no cycles. The case of cycles is of another nature, as the Dulac problem in dimension three.

References:

1.-Alonso, C.; Topological equivalence for Saddle Connections. Qualitative Theory of Dynamical Systems. Accepted: april 2002. To appear 2003.

2.- Alonso, C; Camacho, M.I.T; Cano, F.; Topological Equivalence for Multiple Saddle Connections. Anais da Academia Brasileira de Ciencias. (2002) 74(4):577-584.

3.- Alonso, C.; Equivalencia Topológica para conexiones múltiples de sillas en dimensión tres. Tesis Doctoral. Universidad de Valladolid. 24 Febrero 2003.

Date received: May 27, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # calo-03.