Existence of non-algebraic singularities of differential equation

An algebraizable singularity is a germ of a singular holomorphic foliation which can be defined in some local chart by a differential equation with algebraic coefficients. We show that there exist at least countably many saddle-node singularities of the complex plane that are not algebraizable.

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Bibliographic Details
Published in:Journal of Differential Equations 2010-03, Vol.248 (5), p.1256-1267
Main Authors: Genzmer, Yohann, Teyssier, Loïc
Format: Article
Language:English
Subjects:
Dynamical Systems
Mathematics
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Summary:An algebraizable singularity is a germ of a singular holomorphic foliation which can be defined in some local chart by a differential equation with algebraic coefficients. We show that there exist at least countably many saddle-node singularities of the complex plane that are not algebraizable.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2009.10.001