On algebraic bi-Lipschitz homeomorphisms

2021/04/14 by Zbigniew Jelonek, Jelonek, Zbigniew
Mathematics · #Advanced Differential Equations and Dynamical Systems #Mathematical Dynamics and Fractals #Functional Equations Stability Results

paper · pdf · doi:10.48550/arxiv.2104.06894

Abstract

Let X⊂ ℂⁿ; Y⊂ ℂ^m be closed affine varieties and let ϕ: X→ Y be an algebraic bi-Lipschitz homeomorphism. Then \rm deg X=\rm deg Y. Similarly, let (X,0)⊂ (ℂⁿ,0), (Y,0)⊂ (ℂ^m,0) be germs of analytic sets and let f: (X,0)→ (Y,0) be a c-holomorphic and bi-Lipschitz mapping. Then \rm mult₀ X= \rm mult ₀ Y. Finally we show that the normality is not a bi-Lipschitz invariant.

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