Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Normal forms and embedding problem for some formal transseries

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


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.

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