Quasi-analytic solutions of analytic ordinary differential equations and o-minimal structures

DOI10.1112/PLMS/PDM016zbMath1123.03031arXivmath/0505073OpenAlexW2031160557MaRDI QIDQ5308197

Reinhard Schäfke, Fernando Sanz Sánchez, Jean-Philippe Rolin

Publication date: 27 September 2007

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0505073

zbMATH Keywords

analytic functionso-minimal structurereal analytic vector fieldsnon-oscillating trajectories

Mathematics Subject Classification ID

Asymptotics and summation methods for ordinary differential equations in the complex domain (34M30) Model theory of ordered structures; o-minimality (03C64) Quasi-analytic and other classes of functions of one complex variable (30D60) Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain (34M40)

Related Items (13)

Parabolic curves of diffeomorphisms asymptotic to formal invariant curves ⋮ Trajectories in interlaced integral pencils of 3-dimensional analytic vector fields are o-minimal ⋮ On smooth locally o-minimal functions ⋮ Construction of O-minimal Structures from Quasianalytic Classes ⋮ Course on Non-oscillatory Trajectories ⋮ Theorem of Lion and o-minimal structures which do not admit $\mathcal {C}^{\infty }$-cell decompositions ⋮ Approximations in globally subanalytic and Denjoy-Carleman classes ⋮ Multivariable Newton-Puiseux theorem for generalised quasianalytic classes ⋮ Non-interlaced solutions of 2-dimensional systems of linear ordinary differential equations ⋮ Solitary trajectories of analytic vector fields ⋮ Quantifier elimination and rectilinearization theorem for generalized quasianalytic algebras ⋮ Solutions of definable ODEs with regular separation and dichotomy interlacement versus Hardy ⋮ Solutions of some quasianalytic equations

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