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Preprint Number 634

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634. Olivier Le Gal, Fernando Sanz and Patrick Speissegger
Trajectories in interlaced integral pencils of 3-dimensional analytic vector fields are o-minimal
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Submission date: 8 October 2013.

Abstract:

Let X be an analytic vector field defined in a neighborhood of the origin of R^3, and let I be an analytically non-oscillatory integral pencil of X; that is, I is a maximal family of analytically non-oscillatory trajectories of X at the origin all sharing the same iterated tangents. We prove that if I is interlaced, then for any trajectory T in I, the expansion of the structure generated over the real field by T and all globally subanalytic sets is model-complete, o-minimal and polynomially bounded.

Mathematics Subject Classification: 34C08, 03C64, 34M30

Keywords and phrases:

Full text arXiv 1310.2225: pdf, ps.


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