Existence of non-algebraic singularities of differential equation

Mathematics – Dynamical Systems

Scientific paper

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11 pages

Scientific paper

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

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