Journal of Modern Dynamics (JMD)

The Julia set of a post-critically finite endomorphism of $\mathbb{PC}^2$

Pages: 327 - 375, Issue 3, July 2012      doi:10.3934/jmd.2012.6.327

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Volodymyr Nekrashevych - Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, United States (email)

Abstract: We construct a combinatorial model of the Julia set of the endomorphism $f(z, w)=((1-2z/w)^2, (1-2/w)^2)$ of $\mathbb{PC}^2$.

Keywords:  Post-critically finite endomorphisms, Hubbard trees, Julia set, iterated monodromy groups.
Mathematics Subject Classification:  Primary: 37F20, 37D20; Secondary: 20F65.

Received: April 2011;      Available Online: October 2012.