Transition maps at non-resonant hyperbolic singularities are o-minimal
Dynamical Systems
2009-04-20 v4 Logic
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.
Cite
@article{arxiv.math/0612745,
title = {Transition maps at non-resonant hyperbolic singularities are o-minimal},
author = {Tobias Kaiser and Jean-Philippe Rolin and Patrick Speissegger},
journal= {arXiv preprint arXiv:math/0612745},
year = {2009}
}
Comments
49 pages, 2 figures