Kodai Mathematical Journal

On complex analytic properties of limit sets and Julia sets

Hiroshige Shiga

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Abstract

It is known that Kleinian groups and complex dynamics have many properties in common. We shall show that the structure of the Martin boundaries of the region of discontinuity and the Fatou set are similar under a certain condition. We also show that any conformal mapping defined on the region of discontinuity (resp. the Fatou set) has a continuous extension on the conical limit set (resp. the conical Julia set in the sense of Lyubich and Minsky).

Article information

Source
Kodai Math. J., Volume 28, Number 2 (2005), 368-381.

Dates
First available in Project Euclid: 11 August 2005

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1123767017

Digital Object Identifier
doi:10.2996/kmj/1123767017

Mathematical Reviews number (MathSciNet)
MR2153924

Zentralblatt MATH identifier
1092.37029

Citation

Shiga, Hiroshige. On complex analytic properties of limit sets and Julia sets. Kodai Math. J. 28 (2005), no. 2, 368--381. doi:10.2996/kmj/1123767017. https://projecteuclid.org/euclid.kmj/1123767017


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