Iteration of Rational Functions

The Dynamics of Newton's Method on Complex Quartic Polynomial

Elliptic Functions: The Weierstrass elliptic functions

Newton’s iterative method for finding solutions to nonlinear equations leads to some beautiful images when applied to complex functions. These images represent the basins of attraction of roots of complex functions. The interesting point about the basins of attraction for the roots of a complex function F approximated by relaxed Newton’s method is that they are fractals called Julia sets of a rational function NF,h. The main aim of the present paper is to describe such fractal sets.

Mystery of the rational iteration arising from relaxed Newton’s method

Este trabajo se enmarca en las ´areas de Sistemas Din´amicos Discretos y Geometr´ia Fractal, cada una de estas dos ´areas es bastante amplia con un desarrollo y estudio formal relativa- mente reciente. Los Sistemas Iterados de Funciones y los Sistemas Din´amicos Discretos, constituyen dos m´etodos en cierta forma “duales” para construir Fractales: por una parte fractal como Atrac- tor de un Sistema Iterado de Funciones y por otra fractal como Conjunto de Julia asociado a un Sistema Din´amico Discreto. En el presente art´iculo se muestra como construir un Sistema Iterado de Funciones a partir de un Sistema Din´amico Discreto y viceversa.

https://dialnet.unirioja.es/descarga/articulo/5345979.pdf

Sistemas Iterados de Funciones Vs Sistemas Din´amicos Discretos

We are interested in the Julia set of a semigroup of rational functions with coefficients in $\C_p$ where the semigroup operation is composition We prove that if a semigroup $G$ is generated by a finite number of rational functions of degree at least two with coefficients in a finite extension of $\Q_p$, and has a nonempty Julia set $\cj(G)$, then $\cj(G)$ is perfect and has an empty interior

Iteration of Rational Functions

Citations

The Dynamics of Newton's Method on Complex Quartic Polynomial

Elliptic Functions: The Weierstrass elliptic functions

Mystery of the rational iteration arising from relaxed Newton’s method

Sistemas Iterados de Funciones Vs Sistemas Din´amicos Discretos

SEMIGROUP OF RATIONAL p-ADIC FUNCTIONS FOR COMPOSITION

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