Enriched Riemann sphere, Morse stability and equi-singularity in \(\mathcal O_{2}\) (Q2880394)
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scientific article; zbMATH DE number 6023889
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Enriched Riemann sphere, Morse stability and equi-singularity in \(\mathcal O_{2}\) |
scientific article; zbMATH DE number 6023889 |
Statements
13 April 2012
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fractional power series
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Puiseux expansion
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Morse stability
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Morse singularity
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infinitesimals
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equisingularity
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Newton polygon
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0.89456755
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0.85867995
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0.8581467
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0.8538562
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0.8529049
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0.8525977
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Enriched Riemann sphere, Morse stability and equi-singularity in \(\mathcal O_{2}\) (English)
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The authors extend some basic concepts and results of classical complex analysis and geometry over the ground field of convergent fractional power series. Thus, they generalize Cauchy integral theorem, Taylor expansions, the notion of critical points, Morse lemma and stability theorem, resolutions of singularities, equi-singular deformations of singularities in the plane, etc. In fact, this work is a detail exposition of two notes by the authors [Proc. Japan Acad., Ser. A 81, No. 6, 115--120 (2005; Zbl 1096.14044); C. R. Math. Acad. Sci., Soc. R. Can. 32, No. 4, 120--126 (2010; Zbl 1239.32022)].
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