**abstract:**
In this talk we will present Ecalle’s resurgence theory in application
to dynamics of a simple parabolic germ \(f (z ) = z + z^2 + O(z^3)\).
By definition, Fatou coordinates are conformal solutions of the equation
\(H(f (z )) = H(z ) + 1\) in an attracting and a repelling Fatou petals. The
Ecalle-Voronin invariants describe a relation between the Fatou
coordinates and give a complete invariant of conformal conjugacy of
simple parabolic germs. There is a formal solution H of the Fatou
coordinate equation in terms of divergent series which gives an
asymptotic expansion for the Fatou coordinates of f. The purpose of the
talk is to present the "Bridge equation" which allows to recover
Ecalle-Voronin invariants from H using Ecalle’s Alien Calculus. The work
is in progress (joint with David Sauzin).

Wed 4 May, 11:30 - 12:30, Sala Conferenze Centro De Giorgi

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