arXiv Analytics

Sign in

arXiv:0711.2672 [math.DS]AbstractReferencesReviewsResources

Hyperbolic dimension of Julia sets of meromorphic maps with logarithmic tracts

Krzysztof Barański, Bogusława Karpińska, Anna Zdunik

Published 2007-11-16Version 1

We prove that for meromorphic maps with logarithmic tracts (e.g. entire or meromorphic maps with a finite number of poles from class $\mathcal B$), the Julia set contains a compact invariant hyperbolic Cantor set of Hausdorff dimension greater than 1. Hence, the hyperbolic dimension of the Julia set is greater than 1.

Comments: 7 pages, 1 figure
Journal: Internat. Math. Res. Notices 2009 (2009), 615-624
Categories: math.DS
Subjects: 37F10, 37F35, 30D40, 28A80
Related articles: Most relevant | Search more
arXiv:0712.4267 [math.DS] (Published 2007-12-27)
Hyperbolic dimension and radial Julia sets of transcendental functions
arXiv:0902.1065 [math.DS] (Published 2009-02-06)
Dimension properties of the boundaries of exponential basins
arXiv:1602.08637 [math.DS] (Published 2016-02-27)
Bounded Geometry and Characterization of Some Transcendental Entire and Meromorphic Maps

Links

Toolbox