BookDOI
Iteration of Rational Functions
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This article is published in American Mathematical Monthly.The article was published on 1991-01-01. It has received 972 citations till now. The article focuses on the topics: Elliptic rational functions & Rational function.read more
Citations
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Journal ArticleDOI
Explicit estimates on distance estimator method for Julia sets of polynomials
TL;DR: In this article, the authors give explicit estimates on the accuracy of the distance estimator method, which is well-known as an iterative method which estimates the Euclidean distance between a given point and Julia set.
Journal ArticleDOI
Dynamics of a multipoint variant of Chebyshev-Halley's family
TL;DR: A complex dynamical study of a parametric Chebyshev-Halley type family of iterative methods on quadratic polynomial is presented and the stability of the fixed points is analyzed in terms of the parameter of the family.
Journal ArticleDOI
An Infinite Sequence of Bitransitive Sierpiński Carpets for z↦λ(z + 1 z)
TL;DR: In this article , it was shown that for any distinct pair of such parameter values, the dynamics of the map restricted to the Julia set are not conjugate, however, the Sierpiński carpet fractal is homeomorphic.
Dissertation
Real Analyticity of Hausdorff Dimension of Disconnected Julia Sets of Cubic Parabolic Polynomials
TL;DR: In this paper, a family of cubic parabolic polynomials given by for non-zero complex parameters such that for each the polynomial is a parabolic fixed point and the Julia set of, denoted by, does not contain any critical points of.
Journal ArticleDOI
On the Continuity of Hausdorff Dimension of Julia Sets Concerning Potts Models
Gang Liu,Junyang Gao +1 more
TL;DR: Considering the Julia sets of a family of rational maps concerning two-dimensional diamond hierarchical Potts models in statistical mechanics, this paper showed the continuity of their Hausdorff dimension.