Displaying similar documents to “A natural equivalence relation on singularities”

A remark on the identity principle for analytic sets

Marek Jarnicki, Peter Pflug (2011)

Colloquium Mathematicae

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We present a version of the identity principle for analytic sets, which shows that the extension theorem for separately holomorphic functions with analytic singularities follows from the case of pluripolar singularities.

Constructing blow-analytic isomorphisms

Toshizumi Fukui, Tzee-Char Kuo, Laurentiu Paunescu (2001)

Annales de l’institut Fourier

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In this paper we construct non-trivial examples of isomorphisms and we obtain, via toric modifications, an inverse function theorem in this category. We also show that any analytic curve in ℝ n , n ≥ 3 , can be deformed via a rational blow- analytic isomorphism of ℝ n , to a smooth analytic arc.

Implicit function theorem for locally blow-analytic functions

Laurentiu Paunescu (2001)

Annales de l’institut Fourier

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In this paper we prove the implicit function theorem for , and as an interesting application of using blow-analytic homeomorphisms, we describe a very easy way to resolve singularities of analytic curves.

On movable singularities of self-similar solutions of semilinear wave equations

Radosław A. Kycia (2012)

Banach Center Publications

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In this paper we analyze movable singularities of the solutions of the equation for self-similar profiles resulting from semilinear wave equation. We study local analytic solutions around two fixed singularity points of this equation- ρ = 0 and ρ = 1. The movable singularities of local analytic solutions at the origin will be connected with those of the Lane-Emden equation. The function describing approximately their position on the complex plane will be derived. For ρ > 1 some topological...