Transition maps at non-resonant hyperbolic singularities are o-minimal

Details Transition maps at non-resonant hyperbolic singularities are o-minimal Transition maps at non-resonant hyperbolic singularities are o-minimal

2006-12-23

arxiv.org/abs/math/0612745v4

Mathematics

Dynamical Systems

49 pages, 2 figures

Scientific paper

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.

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