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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Journal ArticleDOI
Preperiodic points for families of polynomials
TL;DR: In this article, the authors studied whether there exist infinitely many complex numbers such that both polynomials with coefficients in complex numbers are preperiodic for one-parameter polynomial families indexed by all complex numbers.
Journal ArticleDOI
Iteration of meromorphic functions
TL;DR: In this article, the authors describe some of the results obtained in the iteration theory of transcendental meromorphic functions, not excluding the case of entire functions, and some aspects where the transcendental case is analogous to the rational case are treated rather briefly here.
Journal ArticleDOI
Geometry and ergodic theory of non-recurrent elliptic functions
Janina Kotus,Mariusz Urbański +1 more
TL;DR: In this article, the authors studied the class of elliptic functions whose critical points all contained in the Julia set are non-recurrent and whose ω-limit sets form compact subsets of the complex plane.
Book ChapterDOI
Static Analysis of the Numerical Stability of Loops
TL;DR: A relational static analysis to determine the stability of the numerical errors arising inside a loop in which floating-point computations are carried out based on a stability test for non-linear functions and on a precise semantics for floating- point numbers that computes the propagation of the errors made at each operation.