Ergodicity in some families of Nevanlinna functions
Volume 265 / 2024
Fundamenta Mathematicae 265 (2024), 179-195
MSC: Primary 37F10; Secondary 30F05, 30D05, 37A30
DOI: 10.4064/fm230929-26-1
Published online: 18 March 2024
Abstract
We study Nevanlinna functions $f$, that is, transcendental meromorphic functions having $N$ asymptotic values and no critical values. Keen and Kotus (1999) proved that if the orbits of all the asymptotic values have accumulation sets that are compact and on which $f$ is a repeller, then $f$ acts ergodically on its Julia set. In the present paper we prove that if some but not all of the asymptotic values have this property, while the others are prepoles, the same holds true. This is the first paper to consider this mixed case.
