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1 October 2014 Minimal Ahlfors regular conformal dimension of coarse expanding conformal dynamics on the sphere
Peter Haïssinsky, Kevin M. Pilgrim
Duke Math. J. 163(13): 2517-2559 (1 October 2014). DOI: 10.1215/00127094-2819408

Abstract

Suppose that f:S2S2 determines a dynamical system on the sphere which is topologically coarse expanding conformal in the sense of our previous work. We prove that if its Ahlfors regular conformal dimension Q is realized by some metric d, then either (i) Q=2 and f is topologically conjugate to a semihyperbolic rational map with Julia set equal to the whole sphere or (ii) Q>2 and f is topologically conjugate to a map which lifts to an affine expanding map of a torus whose differential has distinct real eigenvalues. This is an analogue of a known result for Gromov hyperbolic groups with a two-sphere boundary.

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Peter Haïssinsky. Kevin M. Pilgrim. "Minimal Ahlfors regular conformal dimension of coarse expanding conformal dynamics on the sphere." Duke Math. J. 163 (13) 2517 - 2559, 1 October 2014. https://doi.org/10.1215/00127094-2819408

Information

Published: 1 October 2014
First available in Project Euclid: 1 October 2014

zbMATH: 1384.37056
MathSciNet: MR3265557
Digital Object Identifier: 10.1215/00127094-2819408

Subjects:
Primary: 37F30, 54E40
Secondary: 20F67, 30C65

Rights: Copyright © 2014 Duke University Press

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Vol.163 • No. 13 • 1 October 2014
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