Hausdorff Dimension and Conformal Dynamics III: Computation of Dimension

Hausdorff Dimension and Conformal Dynamics III: Computation of Dimension

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Hausdorff Dimension and Conformal Dynamics III: Computation of Dimension

dc.contributor.author	McMullen, Curtis T.
dc.date.accessioned	2009-12-18T20:55:20Z
dc.date.issued	1998
dc.identifier.citation	McMullen, Curtis T. 1998. Hausdorff dimension and conformal dynamics, III: Computation of dimension. American Journal of Mathematics 120(4): 691-721. Revised 2003.	en_US
dc.identifier.issn	0002-9327	en_US
dc.identifier.uri	http://nrs.harvard.edu/urn-3:HUL.InstRepos:3445973
dc.description.abstract	This paper presents an eigenvalue algorithm for accurately computing the Hausdorff dimension of limit sets of Kleinian groups and Julia sets of rational maps. The algorithm is applied to Schottky groups, quadratic polynomials and Blaschke products, yielding both numerical and theoretical results. Dimension graphs are presented for (a) the family of Fuchsian groups generated by reﬂections in 3 symmetric geodesics; (b) the family of polynomials \(f_c(z) = z^2 +c, c \in [-1, \frac{1}{2}]\); and (c) the family of rational maps \(ft(z) = \frac{z}{t} + \frac{1}{z}, t \in (0, 1]\). We also calculate \(H. dim (\wedge) \approx 1.305688\) for the Apollonian gasket, and \(H. dim (J( f)) \approx 1.3934\) for Douady’s rabbit, where \(f(z) = z^2 + c\) satisﬁes \(f^3(0) = 0\).	en_US
dc.description.sponsorship	Mathematics	en_US
dc.language.iso	en_US	en_US
dc.publisher	Johns Hopkins University Press	en_US
dc.relation.isversionof	doi:10.1353/ajm.1998.0031	en_US
dc.relation.hasversion	http://www.math.harvard.edu/~ctm/papers/index.html	en_US
dash.license	LAA
dc.title	Hausdorff Dimension and Conformal Dynamics III: Computation of Dimension	en_US
dc.type	Journal Article	en_US
dc.description.version	Author's Original	en_US
dc.relation.journal	American Journal of Mathematics	en_US
dash.depositing.author	McMullen, Curtis T.
dc.date.available	2009-12-18T20:55:20Z