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

@misc{citeulike:1711753, 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.}, archivePrefix = {arXiv}, author = {Kaiser, Tobias and Rolin, Jean-Philippe and Speissegger, Patrick}, citeulike-article-id = {1711753}, citeulike-linkout-0 = {http://arxiv.org/abs/math/0612745}, citeulike-linkout-1 = {http://arxiv.org/pdf/math/0612745}, day = {3}, eprint = {math/0612745}, keywords = {abelian\_integrals, complex\_analysis, fewnomials, limit\_cycles, normal\_forms, o-minimal}, month = {May}, posted-at = {2007-09-30 17:20:29}, priority = {3}, title = {Transition maps at non-resonant hyperbolic singularities are o-minimal}, url = {http://arxiv.org/abs/math/0612745}, year = {2007} }

TY - ELEC ID - citeulike:1711753 L3 - citeulike-article-id:1711753 N2 - 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. TI - Transition maps at non-resonant hyperbolic singularities are o-minimal KW - abelian_integrals KW - complex_analysis KW - fewnomials KW - limit_cycles KW - normal_forms KW - o-minimal AU - Kaiser, Tobias AU - Rolin, Jean-Philippe AU - Speissegger, Patrick PY - 2007/May/03/ UR - http://arxiv.org/abs/math/0612745 ER -