Equivalence of differentiable functions, rational functions and polynomials

DOI10.5802/aif.899zbMath0466.58006OpenAlexW2325654683MaRDI QIDQ1155291

Masahiro Shiota

Publication date: 1982

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1982__32_4_167_0

zbMATH Keywords

equivalence to a polynomiallocally equivalent to a germ of a rational functionMilnor number of the germ at each critical pointnumber of critical pointsreal affine non-singular algebraic varietiesright equivalence of smooth functions

Mathematics Subject Classification ID

Theory of singularities and catastrophe theory (58K99) Differentiable maps on manifolds (58C25) Real-valued functions on manifolds (58C05)

Related Items (6)

Classification of Nash manifolds ⋮ Algebraicity of cycles on smooth manifolds ⋮ On analytic equivalence of functions at infinity ⋮ Algebraic cycles and algebraic models of smooth manifolds ⋮ Algebraic models of smooth manifolds ⋮ Real algebraic realization of characteristic classes

Cites Work

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• Equivalence of differentiable mappings and analytic mappings
• Differentiable and combinatorial structures on manifolds
• On the unique factorization property of the ring of Nash functions
• L'équivalence d'une fonction différentiable et d'un polynôme
• On irreducible 3-manifolds which are sufficiently large
• Idéaux de fonctions différentiables. I
• A Certain Region in Euclidean 3-Space

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