Invariant Peano curves of expanding Thurston maps

Daniel Meyer Jacobs University, Campus Ring 1, Bremen, Germany

Classical Analysis and ODEs Complex Variables and Complex Analysis mathscidoc:1701.05001

Acta Mathematica, 210, (1), 95-171, 2010.11
We consider$Thurston maps$, i.e., branched covering maps$f:S$^{2}→$S$^{2}that are$post-critically finite$. In addition, we assume that$f$is$expanding$in a suitable sense. It is shown that each sufficiently high iterate$F$=$f$^{$n$}of$f$is$semi-conjugate$to$z$^{$d$}:$S$^{1}→$S$^{1}, where$d$= deg F. More precisely, for such an$F$we construct a$Peano curve γ$:$S$^{1}→$S$^{2}(onto), such that$F$∘$γ$($z$) =$γ$($z$^{$d$}) (for all$z$∈$S$^{1}).
Expanding Thurston map; Invariant Peano curve
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@inproceedings{daniel2010invariant,
  title={Invariant Peano curves of expanding Thurston maps},
  author={Daniel Meyer},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203400322677767},
  booktitle={Acta Mathematica},
  volume={210},
  number={1},
  pages={95-171},
  year={2010},
}
Daniel Meyer. Invariant Peano curves of expanding Thurston maps. 2010. Vol. 210. In Acta Mathematica. pp.95-171. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203400322677767.
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