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

A. Dolich, and P. Speissegger. "An ordered structure of rank two related to Dulac's Problem." Fundamenta Mathematicae 198.1 (2008): 17-60. <http://eudml.org/doc/286675>.

@article{A2008,
abstract = {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.},
author = {A. Dolich, P. Speissegger},
journal = {Fundamenta Mathematicae},
keywords = {vector fields; limit cycles; model theory; ordered structures; Dulac's Problem},
language = {eng},
number = {1},
pages = {17-60},
title = {An ordered structure of rank two related to Dulac's Problem},
url = {http://eudml.org/doc/286675},
volume = {198},
year = {2008},
}

TY - JOUR
AU - A. Dolich
AU - P. Speissegger
TI - An ordered structure of rank two related to Dulac's Problem
JO - Fundamenta Mathematicae
PY - 2008
VL - 198
IS - 1
SP - 17
EP - 60
AB - 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.
LA - eng
KW - vector fields; limit cycles; model theory; ordered structures; Dulac's Problem
UR - http://eudml.org/doc/286675
ER -