$C^{l}-\mathcal{G}_{V}-$ determinacy of weighted homogeneous function germs on weighted homogeneous analytic varieties
| Autor: | Dun-mu Zhang, Hengxing Liu |
|---|---|
| Rok vydání: | 2008 |
| Předmět: |
Degree (graph theory)
58A35 Mathematics::Complex Variables General Mathematics weighted homogeneous polynomial function germs Homogeneous function Structure (category theory) $C^{l}-\mathcal{R}_{V}$-determinacy Order (ring theory) Function (mathematics) Combinatorics symbols.namesake weighted homogeneous control functions Homogeneous polynomial symbols controlled vector field Germ Variety (universal algebra) $C^{l}-\mathcal{K}_{V}$-determinacy Mathematics |
| Zdroj: | Hokkaido Math. J. 37, no. 2 (2008), 309-329 |
| ISSN: | 0385-4035 |
| DOI: | 10.14492/hokmj/1253539557 |
| Popis: | We provide estimates on the degree of $C^{l}-\mathcal{G}_{V}$-determinacy ($\mathcal{G}$ is one of Mather's groups $\mathcal{R} $ or $\mathcal{K}$) of weighted homogeneous function germs which are defined on weighted homogeneous analytic variety $V$ and satisfies a convenient Lojasiewicz condition. The result gives an explicit order such that the $C^{l}$-geometrical structure of a weighted homogeneous polynomial function germ is preserved after higher order perturbations, which generalize the result on $C^{l}-\mathcal{K}$-determinacy of weighted homogeneous functions germs given by M. A. S. Ruas. |
| Databáze: | OpenAIRE |
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