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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Solution of a problem of Rubel concerning iteration and algebraic differential equations
TL;DR: It is shown in this paper that there does not exist a transcendental entire function with the property that all its iterates satisfy the same algebraic differential equation, which is a question of L. A. Rubel.
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On infinite area for complex exponential function
TL;DR: In this article, the relaxed Newton's method is applied to complex exponential functions F ( z ) = z e z and F( z )= Z e z 2, the basin of roots has infinite area.
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Negativity of Lyapunov Exponents and Convergence of Generic Random Polynomial Dynamical Systems and Random Relaxed Newton's Methods
TL;DR: Under certain conditions on the families, for a generic system, for all but countably many initial values in the Riemann sphere, for almost every sequence of maps $\gamma =(\gamma{1},\gamma_{2},\ldots )$, the Lyapunov exponent of $\gamMA $ at $z$ is negative.
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Hausdorff dimension, strong hyperbolicity and complex dynamics
Shmuel Friedland,Gunter Ochs +1 more
TL;DR: In this paper, the authors show that strong hyperbolicity is structurally stable in the sense that it is the closure of repelling periodic points of the Julia set of compact manifolds.
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A method for studying stability domains in physical models
TL;DR: In this paper, a method for investigating the simultaneous movement of all zeros of equations of motions defined by discrete mappings is presented, which is used to establish periodicities and relative stability properties of the various possible physical solutions.