Analytical invariants of conformal transformations : a dynamical system approach

Preprint enviat per a la seva publicació en una revista científica: Regular & Chaotic Dynamics, 1998, Vol. 3(4), pp.40-48. [https://doi.org/10.1070/RD1998v003n04ABEH000091]The paper is devoted to the problem of analytical classification of conformal maps of the form f: z z+z2+ ... in a neighborhood of the degenerate fixed point z=0. It is shown that the analytical invariants, constructed in the works of Voronin and Ecalle, may be considered as a measure of splitting for stable and unstable (semi-)invariant foliations associated with the fixed point. This splitting is exponentially small with respect to the distance to the fixed point