Real Algebraic and Analytic Geometry

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

e-mail: , ,

Submission: 2006, December 23.

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 (1991): 37C27, 37E35, 03C64.

Keywords and Phrases: Dynamical Systems; Logic.

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