Geometric limits of mixed families
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS(2022)
Abstract
Letting f and h denoting rational maps of degree at least 2 and 1 respectively, and denote by f(n) the nth iterate of f. We give upper and lower bounds on the set of accumulation points of the Julia sets J (h circle f(n)) with respect to the Hausdorff metric on non-empty compact subsets of the sphere.
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Key words
Julia set, geometric limit, Hausdorff convergence, rational iteration
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