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).