𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Iteration of rational functions

✍ Scribed by Beardon A.F.

Book ID
127433314
Year
2000
Tongue
English
Weight
3 MB
Category
Library

No coin nor oath required. For personal study only.

✦ Synopsis

This book makes available a comprehensive, detailed, and organized treatment of the foundations of the theory of iteration of rational functions of a complex variable. The material covered extends from the original memoirs of Fatou and Julia to the recent and important results and methods of Sullivan and Shishikura. Many of the details of the proofs have not occurred in print before. The theory of of dynamical systems and chaos has recently undergone a rapid growth in popularity, in part due to the spectacular computer graphics of Julia sets, fractals, and the Mandelbrot set. This text focuses on the specialized area of complex analytic dynamics, a subject that dates back to 1916 and is currently a very active area in mathematics.

πŸ“œ SIMILAR VOLUMES

Iteration of rational functions
Iteration of rational functions
✍ Alan F. Beardon πŸ“‚ Library πŸ“… 2000 πŸ› Springer 🌐 English βš– 2 MB

This book makes available a comprehensive, detailed, and organized treatment of the foundations of the theory of iteration of rational functions of a complex variable. The material covered extends from the original memoirs of Fatou and Julia to the recent and important results and methods of Sulliva

Rational Functions with a Polynomial Ite
Rational Functions with a Polynomial Iterate
✍ Joseph H. Silverman πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 161 KB

Let ⌽ z g ‫ރ‬ z be a rational function of degree d G 2. A well known theorem n Ε½ . Ε½ . in dynamical systems says that if some iterate z s ( ( ΠΈΠΈΠΈ ( z is a 2 Ε½ . polynomial, then already z is a polynomial. More generally, this is true for Ε½ . Ε½ . Ε½ X Ε½ . . z g K z for any field K provided that is se