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Preprint Number 8

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8. A. Dolich, P. Speissegger
An ordered structure of rank two related to Dulac's problem
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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 UÞ-rank and the other involving the notion of o-minimality.

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