The proposal concerns the topological study of dynamical systems given by multiple saddle-connections of hyperbolic saddles of real vector fields in dimension three. As an application, we would like to obtain results on topological finite determinacy for germs in terms of the principal part given by the Newton Polyhedron, producing, by de-singularization a semi-local problem around the exceptional divisor. After achieving the results concerning multiple saddle-connections guided by an exceptional divisor, without return cycles, we will continue with the following specific problems:
1) Study of the genericity conditions in terms of the Newton Polyhedra that produce suitable multiple saddle-connections after desingularization.
2) Description of the return ma p in case of cycles.
3) Morse-Smale conditions in the interior of the divisor and extension of the topological equivalence from the skeleton.
4) Good coordinates to get the best Newton Polyheda in reach the generic conditions.
5) Inductive methods to pass to higher dimensions.
6) Multiple saddle connections without the guide of a normal crossings divisor.
The proposal contains two years at IMPA and one return year at UVA, under the supervision of C. Camacho and F. Cano, with a specific program of scientific collaborations.
Call for proposal
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