Hölder equivalence of complex analytic curve singularities. Issue 5 (6th August 2018)

• Record Type: Journal Article
• Authors: Fernandes, Alexandre; Sampaio, J. Edson; Silva, Joserlan P.
• Is Part Of: Bulletin of the London Mathematical Society. Volume 50:Issue 5(2018)
• Page Start: 874
• Page End: 886
• Publication Date: 2018-08-06
• Subjects: 14B05 (primary) -- 32S50 (secondary); Mathematics -- Periodicals; 510
• DOI: 10.1112/blms.12192
• Languages: English
• ISSNs: 0024-6093

Abstract

Abstract: We prove that if two germs of irreducible complex analytic curves at 0 ∈ C 2 have 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.