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Preprint Number 8
8. A. Dolich, P. Speissegger
An ordered structure of rank two related to Dulac's problem
Submission date: 10 February 2006, revised version 2 March 2006.
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 UÞ-rank and the other involving the notion of o-minimality.
Mathematics Subject Classification:
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