# Normal forms and embedding problem for some formal transseries

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Jean-Philippe Rolin

created by daniele on 29 Apr 2015

modified on 30 Apr 2015

6 may 2015
-- 14:00

Sala Conferenze, Collegio Puteano, Pisa

Seminari di Dinamica Olomorfa, Pisa

**Abstract.**

Consider a hyperbolic polycycle of an analytic vector field in
the real plane. The asymptotic expansion of its first return map is a
series whose monomials are products of real powers of the variable and
integer powers of its logarithm.
Inspired by motivations arising in fractal analysis, we prove the
existence of (formal) normal forms for such series (considered as
formal diffeomorphisms). Moreover we show that they can be embedded in
the flow of a formal vector field of the same nature.