Normal forms and embedding problem for some formal transseries – Jean-Philippe Rolin (Université de Bourgogne)


Sala Conferenze (Puteano, Centro De Giorgi).


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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