## Journal of the Mathematical Society of Japan

### On Julia sets of postcritically finite branched coverings Part I--coding of Julia sets

Atsushi KAMEYAMA

#### Abstract

We define Julia sets for (topological) expanding postcritically finite branched coverings on $S^{2}$, and show the existence and the uniqueness of Julia sets. Our main aim is the investigation of codings of Julia sets (i.e. semiconjugacies between symbolic dynamics and Julia sets). In particular, it is proved that if two expanding branched coverings are combinatorially equivalent, then their Julia sets are topologically conjugate.

#### Article information

Source
J. Math. Soc. Japan, Volume 55, Number 2 (2003), 439-454.

Dates
First available in Project Euclid: 3 October 2007

https://projecteuclid.org/euclid.jmsj/1191419125

Digital Object Identifier
doi:10.2969/jmsj/1191419125

Mathematical Reviews number (MathSciNet)
MR1961295

Zentralblatt MATH identifier
1162.37318

Subjects
Primary: 37F20: Combinatorics and topology

#### Citation

KAMEYAMA, Atsushi. On Julia sets of postcritically finite branched coverings Part I--coding of Julia sets. J. Math. Soc. Japan 55 (2003), no. 2, 439--454. doi:10.2969/jmsj/1191419125. https://projecteuclid.org/euclid.jmsj/1191419125