Acta Mathematica

Invariant Peano curves of expanding Thurston maps

Daniel Meyer

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We consider Thurston maps, i.e., branched covering maps f:S2S2 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 = fn of f is semi-conjugate to zd: S1S1, where d = deg F. More precisely, for such an F we construct a Peano curve γ: S1S2 (onto), such that Fγ(z) = γ(zd) (for all zS1).

Article information

Acta Math., Volume 210, Number 1 (2013), 95-171.

Received: 4 November 2010
Revised: 25 May 2012
First available in Project Euclid: 31 January 2017

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Zentralblatt MATH identifier

Primary: 37F20: Combinatorics and topology
Secondary: 37F10: Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04]

Expanding Thurston map Invariant Peano curve

2013 © Institut Mittag-Leffler


Meyer, Daniel. Invariant Peano curves of expanding Thurston maps. Acta Math. 210 (2013), no. 1, 95--171. doi:10.1007/s11511-013-0091-0.

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