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Early Days in Complex Dynamics: A history of complex dynamics in one variable during 1906–1942
About this Title
Daniel S. Alexander, Drake University, Des Moines, IA, Felice Iavernaro, Università di Bari, Bari, Italy and Alessandro Rosa
Publication: History of Mathematics
Publication Year:
2011; Volume 38
ISBNs: 978-0-8218-4464-9 (print); 978-0-8218-8325-9 (online)
DOI: https://doi.org/10.1090/hmath/038
MathSciNet review: MR2857586
MSC: Primary 37Fxx; Secondary 01A60, 37-03
Table of Contents
Front/Back Matter
Preliminaries
- A complex dynamics primer
- Introduction: Dynamics of a complex history
- Iteration and differential equations I: The Poincaré connection
- Color plates
- Iteration and differential equations II: Small divisors
The core (1906–1920)
- Early overseas results: The United States
- The road to the Grand Prix des Sciences Mathématiques
- Works written for the Grand Prix
- Iteration in Italy
- The giants fall
After-maths (1920–1942)
- Branching out: Fatou and Julia in the 1920s
- The German wave
- Siegel, the center problem, and KAM theory
- Iteratin’ around the globe
Tying the future to the past
- Report on the Grand Prix des Sciences Mathématiques in 1918
- A history of normal families
- Singular lines of analytic functions
- Kleinian groups
- Curves of Julia
- Progress in Julia’s extension of Schwarz’s lemma
- The Denjoy-Wolff theorem
- Dynamics of self-maps of the unit disc
- Koebe and uniformization
- Permutable maps in the 1920s
- The last 60 years in permutable maps
- Understanding Julia sets of entire maps
- Fatou: A biographical sketch
- Gaston Julia: A biographical sketch
- Selected biographies
- Remarks on computer graphics