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Preprint Number 40

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40. Tobias Kaiser, Jean-Philippe Rolin and Patrick Speissegger
Transition maps at non-resonant hyperbolic singularities are o-minimal

Submission date: 23 December 2006

Abstract:

We construct a model complete and o-minimal expansion of the field of real numbers such that, for any planar analytic vector field X and any isolated, non-resonant hyperbolic singularity p of X, a transition map for X at p is definable in this structure. This structure also defines all convergent generalized power series with natural support and is polynomially bounded.

Mathematics Subject Classification: 37C27, 37E35, 03C64

Keywords and phrases: Dynamical Systems; Logic

Full text: arXiv.


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