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Showing 1 to 3 of 3 for “"Fatou set"”.
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Dynamics and Measures for Semigroups of Rational Functions
… examples of rational semigroups where the Fatou set contains an arbitrary finite number of components. The Fatou set of a single rational function must contain zero, one, two or infinitely many components.
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Dynamics of Cubic Rational Maps Under Certain Constraints on Critical Points
<p>There is a neat dichotomy for the Julia sets of quadratic rational maps; that is, they are either connected or a Cantor set. In contrast to the quadratic case, the Julia sets of rational maps of of degree ≥ 3 have more variations. In this project, we study the Julia sets of cubic rational maps …
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Rates Of Escape Under Iteration Of Analytic Functions
In this thesis we focus on sets with a uniform rate of escape under the iteration of transcendental entire functions. We study their properties and their structure as well as using them as a tool to prove some interesting topological results. First, motivated by the work of Rippon and Stallard, we …