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Formal linearization of logarithmic transseries and analytic linearization of Dulac germs

First we consider formal linearization problem for hyperbolic logarithmic transseries. In particular, we give necessary and sufficient condition for such logarithmic transseries to be formally linearized. Formal linearization is obtained using fixed point theorems. Afterwards we consider analytic linearization problem for analytic germs on invariant complex domains with certain hyperbolic asymptotic bounds. In the end we consider Dulac germs, i.e. analytic germs defined on sufficiently big complex domains which have power-logarithmic asymptotic expansions. In particular, the first return maps of hyperbolic polycycles of analytic planar vector fields are Dulac germs. We apply these formal and analytic linearization results to solve the linearization problem for hyperbolic Dulac germs. This is joint work with M. Resman, J.-P. Rolin and T. Servi.

logarithmic transseries, linearization, formal and analytic classification, (complex) Dulac germs, Dulac series, standard quadratic domains, iteration theory, Koenigs sequence

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