Submission date: 10 February 2006, revised version 2 March 2006.

Abstract:

For a vector field ξ on R² we construct, under certain assumptions on ξ, an ordered model-theoretic structure associated to the flow of ξ. We do this in such a way that the set of all limit cycles of ξ is represented by a definable set. This allows us to give two restatements of Dulac's Problem for ξ --- that is, the question whether ξ has finitely many limit cycles --- in model-theoretic terms, one involving the recently developed notion of U^Þ-rank and the other involving the notion of o-minimality.

Mathematics Subject Classification:

Keywords and phrases

Full text: pdf, dvi, ps. (Old version: pdf, dvi, ps.)