Analitical Invariants of Conformal Transformations. A Dynamical System Approach
1998, Volume 3, Number 4, pp. 40-48
Author(s): Gelfreich V. G.
Author(s): Gelfreich V. G.
The paper is devoted to the problem of analytical classification of conformal maps of the form $f : z \mapsto z + z^2 +\ldots$ 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.
Download File PDF, 305.54 Kb |