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Hölder equivalence of complex analytic curve singularities
Author(s) -
Fernandes Alexandre,
Sampaio J. Edson,
Silva Joserlan P.
Publication year - 2018
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12192
Subject(s) - mathematics , gravitational singularity , multiplicity (mathematics) , plane curve , pure mathematics , equivalence (formal languages) , complex plane , lipschitz continuity , invariant (physics) , sequence (biology) , intersection (aeronautics) , mathematical analysis , complete intersection , mathematical physics , biology , engineering , genetics , aerospace engineering
We prove that if two germs of irreducible complex analytic curves at 0 ∈ C 2have different sequence of characteristic exponents, then there exists 0 < α < 1 such that those germs are not α ‐Hölder homeomorphic. For germs of complex analytic plane curves with several irreducible components we prove that if any two of them are α ‐Hölder homeomorphic, for all 0 < α < 1 , then there is a correspondence between their branches preserving sequence of characteristic exponents and intersection multiplicity of pair of branches. In particular, we recover the sequence of characteristic exponents of the branches and intersection multiplicity of pair of branches are Lipschitz invariant of germs of complex analytic plane curves.