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
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Connectedness and Stability of the Julia Sets of the Composition of Polynomials of Type E d
TL;DR: In this paper, the authors studied the topological properties and stability of the Julia set J(cn) of the composition of polynomials of type Ed. Mathematics Subject Classification: Primary 37F25, secondary 58F23, 32H50.
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Pointwise-recurrent dendrite maps
TL;DR: In this paper, it was shown that if a dendrite is countable (resp. B(D) is discrete) then f is pointwise-recurrent if and only if f is a pointwise periodic homeomorphism.
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Algorithms for computing basins of attraction associated with a rational self-map of the Hopf fibration based on Lyapunov exponents
TL;DR: In this article , the authors developed a theory of iteration for complex rational functions so that the problems of overflow and indeterminacy caused by null, or almost null, denominators can be avoided when developing implementations.
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Electrical networks on n-simplex fractals
TL;DR: In this article, the decimation map for a network of admittances on an n-simplex lattice fractal is studied, and the asymptotic behaviour of large-size fractals is examined.
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Best possibility of the Fatou-Shishikura inequality for transcendental entire functions in the Speiser class
Masashi Kisaka,Hiroto Naba +1 more
TL;DR: The Speiser class is the set of all entire functions with finitely many singular values and gives an upper bound to the Fatou-Shishikura inequality for the Speiser content-type.