Measurable dynamics of meromorphic maps

We study how the orbits of the singularities of the inverse of a meromorphic function prescribe the dynamics on its Julia set, at least up to a set of (Lebesgue) measure zero. We concentrate on a family of entire transcendental functions with only finitely many singularities of the inverse, counting multiplicity, all of which either escape exponentially fast or are pre-periodic. For these functions we are able to decide, whether the function is recurrent or not. In the case that the Julia set is not the entire plane we also obtain estimates for the measure of the Julia set. MSC: 37F10}

Preview

Rights

Use and reproduction:

No license. The provisions of the German Copyright Act (UrhG) apply.

Please note that individual components of the publication may be subject to other licensing or copyright conditions.

Cite

Citation style:
Could not load citation form.