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

DOI10.1515/CRELLE.2009.081zbMath1203.03051arXivmath/0612745OpenAlexW2963963729MaRDI QIDQ3404361

Tobias Kaiser, Patrick Speissegger, Jean-Philippe Rolin

Publication date: 9 February 2010

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612745

zbMATH Keywords

o-minimal structuretransition mapmodel-complete structurenon-resonant hyperbolic singularity

Mathematics Subject Classification ID

Real-analytic and semi-analytic sets (14P15) Model theory of ordered structures; o-minimality (03C64) Analytic subsets of affine space (32B15)

Related Items (19)

Conformal mapping of o-minimal corners ⋮ Ilyashenko algebras based on transserial asymptotic expansions ⋮ Fractal analysis of hyperbolic saddles with applications ⋮ Stratified reduction of singularities of generalized analytic functions ⋮ Stratification of three-dimensional real flows I: fitting domains ⋮ On smooth locally o-minimal functions ⋮ Course on Non-oscillatory Trajectories ⋮ Unnamed Item ⋮ Singularities of o-minimal Peano derivatives ⋮ Smooth functions in o-minimal structures ⋮ Łojasiewicz-type inequalities in complex analysis ⋮ o-minimal analytic separation of sets in dimension 2 ⋮ The Dirichlet problem in the plane with semianalytic raw data, quasi analyticity, and o-minimal structure ⋮ Multivariable Newton-Puiseux theorem for generalised quasianalytic classes ⋮ Development of a new concept of polar analytic functions useful in Mellin analysis ⋮ Whitney's extension problem in o-minimal structures ⋮ Quantifier elimination and rectilinearization theorem for generalized quasianalytic algebras ⋮ The number of limit cycles for regularized piecewise polynomial systems is unbounded ⋮ Piecewise Weierstrass preparation and division for o-minimal holomorphic functions

Cites Work

• The Field of Reals with Multisummable Series and the Exponential Function
• The real field with convergent generalized power series
• Centennial History of Hilbert's 16th Problem

This page was built for publication: Transition maps at non-resonant hyperbolic singularities are o-minimal