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

By T. Kaiser, J. Rolin, Patrick Speissegger. 2006

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

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8d4757060bcbfc88485fc6c972f2ae2a7d5cd16a