Dynamics in One Complex Variable

Beschreibung

This text studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. It is based on introductory lectures given by the author at Stony Brook, NY, in the past ten years.
The subject is large and rapidly growing. These notes are intended to introduce the reader to some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. The exposition is clear and enriched by many beautiful illustrations.


This text studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. It is based on introductory lectures given by the author at Stony Brook, NY, in the past ten years.
The subject is large and rapidly growing. These notes are intended to introduce the reader to some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. The exposition is clear and enriched by many beautiful illustrations.


Milnor's Textbook on Dynamics
Dies ist ein Buch eines bekannten amerikanischen Mathematikers, das aus seiner langjährigen Vorlesungspraxis und seinen Forschungen am Institute for Mathematical Sciences in Stony Brook, NY, als Lehrbuch für Studenten konzipiert wurde. Elementare Kenntnisse aus der Funktionentheorie, Differentialgeometrie, Topologie sind nur erforderlich, um dieses sehr gut geschriebene Buch verstehen zu können. Der Stil von John Milnors Büchern wird allgemein sehr geschätzt. Das Gebiet ist aktuell, es steht in Verbindung mit der mathematischen Theorie der Fraktale. Stichpunkte aus dem Inhalt: Riemannsche Flächen, Iterierte holomorphe Abbildungen, Lokale Fixpunkttheorie, Periodische Punkte: Globale Theorie, Struktur der Fatou Menge, Julia Menge.

Autor*in

John Milnor

Themen in »Dynamics in One Complex Variable«

Dynamisches System Komplexe Analysis Riemann surface differential geometry dynamical systems dynamics geometry mathematics surface surfaces

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