Trajectories in interlaced integral pencils of 3-dimensional analytic vector fields are o-minimal

10 Oct 2017  ·  Gal Olivier Le, Sanz Fernando, Speissegger Patrick ·

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...

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Classical Analysis and ODEs Logic