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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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$C^*$-algebras associated with algebraic correspondences on the Riemann sphere
Tsuyoshi Kajiwara,Yasuo Watatani +1 more
TL;DR: In this article, the authors introduce algebraic correspondences on the Riemann sphere and show that if an algebraic correspondence is free and expansive on a closed $p$-invariant subset $J$ of a given subset of a function, then the associated algebra is simple and purely infinite.
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Consecutive Ratios in Second-Order Linear Recurrence Sequences
Daniel Berend,Rishi Kumar +1 more
TL;DR: In this article , the limit points and asymptotic distribution of the sequence of consecutive ratios an+1/an were studied for a second-order linear recurrence sequence with constant coefficient.
Siegel Discs in Complex Dynamics
TL;DR: In this paper, a siegel disc is shown to be a disjoint union of invariant curves, and it is shown that all limit functions of {fn}n>0 are non-constant.
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Slow escaping points of meromorphic functions
P. J. Rippon,Gwyneth M. Stallard +1 more
TL;DR: In this paper, it was shown that for any transcendental meromorphic function, there is a point in the Julia set of the function that the iterates tend to escape arbitrarily slowly.
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Dynamics of the Secant map near infinity
Antonio Garijo,Xavier Jarque +1 more
TL;DR: In this article , the authors investigated the root finding algorithm given by the Secant method applied to a real polynomial p of degree k as a discrete dynamical system defined on the real projective plane.