Blow-analytic equivalence versus contact bi-Lipschitz equivalence

Birbrair, Lev; Fernandes, Alexandre; Grandjean, Vincent; Gaffney, Terence

doi:10.2969/jmsj/74237423

Cited by 3 publications

(1 citation statement)

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“…The paper is devoted to Lipschitz geometry of real analytic functions. In [3] the authors proved that for analytic functions of two variables the notions of Lipschitz K-equivalence and blow-analytic equivalence coincide. The paper [2] is devoted to classification of germs of subanalytic functions of 2 variables up to Lipschitz K-equivalence.…”

Section: Introductionmentioning

confidence: 99%

Lipschitz contact equivalence and real analytic functions

Birbrair,

Mendes

2018

Preprint

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We study the properties of the a complete invariant of the analytic function of two variables with respect to the Lipschitz contact equivalence. This invariant is called pizza. We prove that the pizza of real analytic functions has some continuity properties. of Valette's link, such that for any two arcs γ 1 , γ 2 in the zone, all the arc, belonging to the Hölder triangle, bounded by γ 1 and γ 2 also belongs to the zone. We are interested in the zones defined by arcs such that the order of a function f on all these arcs is constant. An arc, belonging to the zone Z is called generic, if it belongs to a Hölder triangle, generated by a pair of the other arcs to the zone, such that the order of contact of these two arcs and the order of contact of any one of these with the given arc is equal to the size of the zone. Our main result is that for an analytic function, any arc belonging to any zone of

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Section: Introductionmentioning

confidence: 99%