IJPAM: Volume 106, No. 3 (2016)
FUNCTIONS WHICH CONTAINS KOEBE FUNCTION
Department of Mathematics
Abstract. We study the dynamics of a parameterized family of quadratic rational functions , . We have investigated the dynamical and geometric properties of Julia sets and the nature of the variance of these properties according to the parameter. We have shown the Julia sets are connected when and are dynamically defined cantor sets when . We also have shown the continuity of geometric properties specially in terms of Hausdorff dimensions of these Julia sets.
Received: November 28, 2015
AMS Subject Classification: 37F
Key Words and Phrases: Julia sets, Hausdorff dimension, bifurcation, Cantor sets
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DOI: 10.12732/ijpam.v106i3.13 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 873 - 881