Complex analytic dynamics on the Riemann sphere
TLDR
In this paper, the authors define a dynamique dynamique de Fatou et Julia, which is defined as the dynamique of points periodiques repulseurs of a group of polynomes.Abstract:
Dichotomie dynamique de Fatou et Julia. Points periodiques. Consequences du theoreme de Montel. L'ensemble de Julia est la fermeture de l'ensemble des points periodiques repulseurs. Resultats classiques sur l'ensemble de Fatou. Classification de Sullivan de l'ensemble de Fatou. Une condition pour le developpement sur l'ensemble de Julia. La dynamique des polynomes. L'ensemble de Mandelbrot et le travail de Douady et Hubbard. Le theoreme d'application de Riemann mesurable et la dynamique analytiqueread more
Citations
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Journal ArticleDOI
On a theory of computation and complexity over the real numbers: $NP$- completeness, recursive functions and universal machines
Book
Complex Dynamics and Renormalization
TL;DR: In this article, the authors present a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics, including geometric function theory, quasiconformal mappings, and hyperbolic geometry.
Journal ArticleDOI
Theory of Functions
TL;DR: In this paper, the authors pointed out that the distinction between "finite" and "infinite" is one which does not require definition, and that the authors' view is not the only accepted view.
Journal ArticleDOI
Iteration of meromorphic functions
TL;DR: In this paper, 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
On the dynamics of polynomial-like mappings
Adrien Douady,John H. Hubbard +1 more
TL;DR: In this article, a parametre d'applications de type polynomial is defined and a set of applications of M dans M. Carrottes pour le dessert are presented.
References
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Book
The Fractal Geometry of Nature
TL;DR: This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.
Journal ArticleDOI
The Fractal Geometry of Nature
TL;DR: A blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) is presented in this article.
Book
Methods of Bifurcation Theory
Shui-Nee Chow,Jack K. Hale +1 more
TL;DR: In this paper, the static and dynamic aspects of bifurcation theory, which are of particular pertinence to differential equations, have been discussed, and a discussion of the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied.
Book
Lectures on quasiconformal mappings
TL;DR: The Ahlfors Lectures: Acknowledgments Differentiable quasiconformal mappings The general definition Extremal geometric properties Boundary correspondence The mapping theorem Teichmuller spaces Editors' notes.