Hausdorff dimensions of the Julia sets of reluctantly recurrent rational maps

Huaibin Li ()
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Huaibin Li: Henan University

Indian Journal of Pure and Applied Mathematics, 2013, vol. 44, issue 6, 849-863

Abstract: Abstract In this paper, we consider a rational map f of degree at least two acting on Riemman sphere that is expanding away from critical points. Assuming that all critical points of f in the Julia set J(f) are reluctantly recurrent, we prove that the Hausdorff dimension of the Julia set J(f) is equal to the hyperbolic dimension, and the Lebesgue measure of Julia set is zero when the Julia set J(f) ≠ .

Keywords: Rational maps; Julia sets; Hausdorff dimension; hyperbolic dimension (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s13226-013-0046-3

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