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Ergodicity in some families of Nevanlinna functions

Volume 265 / 2024

Tao Chen, Yunping Jiang, Linda Keen 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.

Authors

  • Tao ChenDepartment of Mathematics
    Engineering and Computer Science
    LaGuardia Community College, CUNY
    Long Island City, NY 11101, USA
    and
    CUNY Graduate Center
    New York, NY 10016, USA
    e-mail
  • Yunping JiangDepartment of Mathematics
    Queens College of CUNY
    Flushing, NY 11367, USA
    and
    Department of Mathematics
    CUNY Graduate Center
    New York, NY 10016, USA
    e-mail
  • Linda KeenDepartment of Mathematics
    CUNY Graduate Center
    New York, NY 10016, USA
    e-mail
    e-mail

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