Superexact asymptotic series and monodromy maps of the polycycles
A polycycle is a separatrix polygone of a vector field in the plane. Its monodromy transformation
is an analog of the Poincare map for a limit cycle. The difference is that the second map is
defined on an interval, and the first one on a half-interval. In the analytic case, the second map may be decomposed
in a Taylor series. The first one is much more complicated, and may have a correction (difference
with identity) equal to a tower of exponents. Namely, the first map may have a form
Δ(x)=x+f∘n0(x) for arbitrary n; here f0=exp(−1x). Very specific
asymptotic series for these maps will be described in the talk.