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BURIED SIERPINSKI CURVE JULIA SETS
"... Abstract. In this paper we prove the existence of a new type of Sierpinski curve Julia set for certain families of rational maps of the complex plane. In these families, the complementary domains consist of open sets that are preimages of the basin at ∞ as well as preimages of other basins of attrac ..."
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Cited by 3 (1 self)
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Abstract. In this paper we prove the existence of a new type of Sierpinski curve Julia set for certain families of rational maps of the complex plane. In these families, the complementary domains consist of open sets that are preimages of the basin at ∞ as well as preimages of other basins
Mappings of the Sierpinski curve onto itself
 Proc. Amer. Math. Sot
, 1984
"... ABSTRACT. Given two points p and q of the Sierpin'ski universal plane curve S, necessary and/or sufficient conditions are discussed in the paper under which there is a mapping f of S onto itself such that f(p) = q and f belongs to one of the following: homeomorphisms, local homeomorphisms, lo ..."
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Cited by 2 (0 self)
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ABSTRACT. Given two points p and q of the Sierpin'ski universal plane curve S, necessary and/or sufficient conditions are discussed in the paper under which there is a mapping f of S onto itself such that f(p) = q and f belongs to one of the following: homeomorphisms, local homeomorphisms
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 diff ..."
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Cited by 5 (1 self)
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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
Sierpinski Curve Julia Sets and Singular Perturbations of Complex Polynomials
 Systems
, 2003
"... this paper we consider the family of rational maps F (z) = z z where z 2 C and is a parameter. Our goal is to investigate the Julia set of F , which we denote by J(F ). By de nition, J(F ) is the set of points in C at which the family of iterates of F fails to be a normal family in the ..."
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Cited by 19 (9 self)
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this paper we consider the family of rational maps F (z) = z z where z 2 C and is a parameter. Our goal is to investigate the Julia set of F , which we denote by J(F ). By de nition, J(F ) is the set of points in C at which the family of iterates of F fails to be a normal family in the sense of Montel. Equivalently, J(F ) is the closure of the set of repelling periodic points of F . It is also the set on which F behaves chaotically. The complement of the Julia set is called the Fatou set
Cantor Necklaces and Structurally Unstable Sierpinski Curve Julia Sets for Rational Maps
"... In this paper we consider families of rational maps of degree 2n on the Riemann sphere F * : C! C given by F*(z) = z n zn where * 2 C \Gamma f0g and n * 2. The case where n = 1 is very different and hence is excluded from this study. We denote the family of all such rational maps of degree 2n by \L ..."
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Cited by 3 (3 self)
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In this paper we consider families of rational maps of degree 2n on the Riemann sphere F * : C! C given by F*(z) = z n zn where * 2 C \Gamma f0g and n * 2. The case where n = 1 is very different and hence is excluded from this study. We denote the family of all such rational maps of degree 2n by \Lambda n. A function in \Lambda n is called a singular perturbation of z n
Cantor and Sierpinski, Julia and Fatou: Complex Topology Meets Complex Dynamics
"... 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 ..."
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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
Locally Sierpinski Julia Sets of Weierstrass Elliptic P Functions
 International Journal of Bifurcation and Chaos
"... Abstract. We define a locally Sierpinski Julia set to be a Julia set of an elliptic function which is a Sierpinski curve in each fundamental domain for the lattice. In order to construct examples, we give sufficient conditions on a lattice for which the corresponding Weierstrass elliptic ℘ functi ..."
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Cited by 4 (0 self)
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Abstract. We define a locally Sierpinski Julia set to be a Julia set of an elliptic function which is a Sierpinski curve in each fundamental domain for the lattice. In order to construct examples, we give sufficient conditions on a lattice for which the corresponding Weierstrass elliptic
Cantor and Sierpinski, Julia and Fatou: Complex Topology Meets Complex Dynamics
, 2003
"... 1 1 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 objec ..."
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1 1 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
Eikonal equations on the Sierpinski gasket
, 2014
"... We study the eikonal equation on the Sierpinski gasket in the spirit of the construction of the Laplacian in Kigami [8]: we consider graph eikonal equations on the prefractals and we show that the solutions of these problems converge to a function defined on the fractal set. We characterize this lim ..."
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We study the eikonal equation on the Sierpinski gasket in the spirit of the construction of the Laplacian in Kigami [8]: we consider graph eikonal equations on the prefractals and we show that the solutions of these problems converge to a function defined on the fractal set. We characterize
Harmonic functions on the Sierpinski triangle
, 2014
"... In this paper, we give a few results on the local behavior of harmonic functions on the Sierpinski triangle more precisely, of their restriction to a side of the triangle. First we present a general formula that gives the Hölder exponent of such a function in a given point. From this formula, we de ..."
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In this paper, we give a few results on the local behavior of harmonic functions on the Sierpinski triangle more precisely, of their restriction to a side of the triangle. First we present a general formula that gives the Hölder exponent of such a function in a given point. From this formula, we
Results 1  10
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