Sierpi\'{n}ski curve Julia sets for quadratic rational maps
R. L. Devaney, N. Fagella, A. Garijo, X. Jarque
TL;DR
This paper explores the specific dynamical conditions under which the Julia set of quadratic rational maps forms a Sierpiński curve, contributing to the understanding of complex fractal structures in dynamical systems.
Contribution
It identifies the precise conditions that lead to Julia sets being Sierpiński curves in quadratic rational maps, advancing the classification of these fractals.
Findings
Characterization of dynamical conditions for Sierpiński curve Julia sets
Identification of parameter regimes producing Sierpiński Julia sets
Enhanced understanding of fractal structures in quadratic rational dynamics
Abstract
We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpi\'{n}ski curve
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems · Quantum chaos and dynamical systems