# Explicit linearization of one-dimensional germs through tree-expansions”

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Frédéric Fauvet

created by calamai on 24 May 2015

29 may 2015
-- 14:30

Aula 2, DiMai, Firenze

**Abstract.**

We revisit the classical linearization problem of non-resonant
germs of diffeomorphisms in one complex dimension, which contains the
well-known difficulties due to the so-called small divisor phenomenon. Using
a small part of J. Ecalle's ``arbomould formalism'', we obtain explicit
tree--indexed formulas for the transformations involved, which yield Yoccoz's
lower bound for the radius of convergence of the linearization; moreover, we
reach a new global regularity result with respect to the multiplier
($C^1$--holomorphy).