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

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Dolich A., Speissegger P.

Fundamenta Mathematicae

2008

tom 198

nr 1

17-60

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 $U^{þ}$-rank and the other involving the notion of o-minimality.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Dolich A.

1 Speissegger P.

1 2008

Wyniki wyszukiwania

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