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

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