Symbolic dynamics for a Sierpinski curve Julia set
نویسندگان
چکیده
منابع مشابه
Symbolic dynamics for a Sierpinski curve Julia set
In this paper we investigate the dynamics of certain rational functions on their Julia sets. We pay particular attention to the case where the Julia set is a Sierpinski curve. In this case, any two such Julia sets are known to be homeomorphic. However, the dynamics on these sets are often quite different. In this paper, we use symbolic dynamics to show how these different dynamical behaviors ma...
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sends the point z ∈ C to its inversion image about the circle of radius r ∈ R centered at the point a ∈ C. Dynamically, this map is not interesting since iterating twice yields the identity mapping. Using three circles we invert a point z about each circle and form a new map by sending z to the arithmetic mean of the three inversion images. We refer to this as inverting z about the three circle...
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Introduction Topologists have enjoyed pondering the exotic properties of fascinating objects such as indecomposable continua, Sierpinski curves, and Cantor bouquets for almost one hundred years, while complex dynamicists have only recently begun to enjoy the beauty and intricacy of fractal objects known as the Julia sets. Recent developments, however, have brought both of these fields closer to...
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Introduction Topologists have enjoyed pondering the exotic properties of fascinating objects such as indecomposable continua, Sierpinski curves, and Cantor bouquets for almost one hundred years, while complex dynamicists have only recently begun to enjoy the beauty and intricacy of fractal objects known as the Julia sets. Recent developments, however, have brought both of these fields closer to...
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ژورنال
عنوان ژورنال: Journal of Difference Equations and Applications
سال: 2005
ISSN: 1023-6198,1563-5120
DOI: 10.1080/10236190412331334473