An ordered structure of rank two related to Dulac's problem

Details An ordered structure of rank two related to Dulac's problem An ordered structure of rank two related to Dulac's problem

2006-03-02

arxiv.org/abs/math/0603052v2

Mathematics

Logic

45 pages, final version

Scientific paper

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

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