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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2008 | 198 | 1 | 17-60

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

EN

### Abstrakty

EN
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.

17-60

wydano
2008

### Twórcy

autor
• Department of Mathematics, Chicago State University, Chicago, IL 60628, U.S.A.
autor
• Department of Mathematics & Statistics, McMaster University, Hamilton, ON, Canada L8S 4K1