Hausdorff Dimension and Conformal Dynamics III: Computation of Dimension

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Hausdorff Dimension and Conformal Dynamics III: Computation of Dimension

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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

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  • FAS Scholarly Articles [7103]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University

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