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

• Autorzy: A. Dolich , P. Speissegger
• Języki publikacji: 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.

Kategorie tematyczne

• 37C27: Periodic orbits of vector fields and flows
• 03C64: Model theory of ordered structures; o-minimality

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2008
• Tom: 198
• Numer: 1
• Strony: 17-60

Daty

wydano

2008

Twórcy

autor

A. Dolich

• Department of Mathematics, Chicago State University, Chicago, IL 60628, U.S.A.

autor

P. Speissegger

• Department of Mathematics & Statistics, McMaster University, Hamilton, ON, Canada L8S 4K1

Identyfikatory

DOI

10.4064/fm198-1-2