An Ordered Structure of Rank Two Related to Dulac's Problem
نویسنده
چکیده
For a vector eld ξ on R we construct, under certain assumptions on ξ, an ordered model-theoretic structure associated to the ow of ξ. We do this in such a way that the set of all limit cycles of ξ is represented by a de nable set. This allows us to give two restatements of Dulac's Problem for ξ that is, the question whether ξ has nitely 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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