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Preprint Number 8
8. A. Dolich, P. Speissegger An ordered structure of rank two related to Dulac's problem Email: Submission date: 10 February 2006, revised version 2 March 2006. Abstract: For a vector field ξ on R^{2} we construct, under certain assumptions on ξ, an ordered modeltheoretic 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 modeltheoretic terms, one involving the recently developed notion of U^{Þ}rank and the other involving the notion of ominimality. Mathematics Subject Classification: Keywords and phrases

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