RT info:eu-repo/semantics/article
T1 Quasi-analytic solutions of analytic ordinary differential equations and o-minimal structures
A1 Rolin, J.-P.
A1 Sanz, F.
A1 Schäfke, R.
AB It is well known that the non-spiraling leaves of real analytic foliations of codimension 1 all belong to the same o-minimal structure. Naturally, the question arises of whether the same statement is true for non-oscillating trajectories of real analytic vector fields.We show, under certain assumptions, that such a trajectory generates an o-minimal and model-complete structure together with the analytic functions. The proof uses the asymptotic theory of irregular singular ordinary differential equations in order to establish a quasi-analyticity result from which the main theorem follows.As applications, we present an infinite family of o-minimal structures such that any two of them do not admit a common extension, and we construct a non-oscillating trajectory of a real analytic vector field in R5 that is not definable in any o-minimal extension of R.
PB London Mathematical Society
SN 0024-6115
YR 2007
FD 2007
LK https://uvadoc.uva.es/handle/10324/68189
UL https://uvadoc.uva.es/handle/10324/68189
LA eng
NO Proc. London Math. Soc. (3) 95 (2007) 413–442
DS UVaDOC
RD 22-nov-2024