Vortrag im Schwerpunkt Reelle Geometrie und Algebra
Donnerstag, 13. Dezember 2007, um 17:00 Uhr in F426 (Schwerpunktkolloquium) Patrick Speissegger (Hamilton/Zürich) An Ordered Structure of Rank Two Related to Dulac's Problem
ABSTRACT: For a vector field F on the real plane we construct, under certain
assumptions on F, an ordered model-theoretic structure
associated to the flow of F. We do this in such a way that the
set of all limit cycles of F is represented by a definable set.
This allows us to give two restatements of Dulac's Problem for
F--that is, the question whether F has finitely many limit
cycles--in model-theoretic terms, one involving the recently
developed notion of thorn-rank and the other involving the notion
of o-minimality. (Joint work with Alf Dolich)
