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An Isaac Newton Institute Programme

Model Theory and Applications to Algebra and Analysis

Non-oscillating solutions of differential equations and o-minimality

25th May 2005

Author: Rolin, Jean-Philippe (Universite de Bourgogne)

Abstract

We study the behaviour of solutions of analytic differential equations from the point of vue of o-minimality. It is well known that the structure generated by the non spiraling leaves of codimension 1 analytic foliations is o-minimal. We investigate the properties of non oscillating trajectories of analytic vector fields. We show that, under some sufficient conditions related to the notion of quasi-analyticity, these trajectories belong to o-minimal structures. We also give some examples of non oscillating trajectories which do not belong to any o-minimal structure, and examples of infinite families of o-minimal structures such that any two of them do not admit an o-minimal common extension.