IDENTIFYING LOGARITHMIC TRACTS

摘要

We show that a direct tract bounded by a simple curve is a logarithmic tract and further give sufficient conditions for a direct tract to contain logarithmic tracts. As an application of these results, it is shown that an example of a function with infinitely many direct singularities, but no logarithmic singularity over any finite value, is in the Eremenko Lyubich class.