Abstract
We study the dynamics of a parameterized family of quadratic rational functions z 7→�z/(1−z) 2 , � ∈ (0,∞). 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 � > 1 and are dynamically defined cantor sets when � < 1. We also have shown the continuity of geometric properties specially in terms of Hausdorff dimensions of these Julia sets.
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