Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Explicit linearization of one-dimensional germs through tree-expansions”

Frédéric Fauvet

created by calamai on 24 May 2015

29 may 2015 -- 14:30

Aula 2, DiMai, Firenze


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).

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