**History of Mathematics**

Volume: 38;
2011;
454 pp;
Hardcover

MSC: Primary 01; 30;
**Print ISBN: 978-0-8218-4464-9
Product Code: HMATH/38**

List Price: $104.00

Individual Member Price: $83.20

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#### Supplemental Materials

# Early Days in Complex Dynamics: A history of complex dynamics in one variable during 1906–1942

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*Daniel S. Alexander; Felice Iavernaro; Alessandro Rosa*

A co-publication of the AMS and the London Mathematical Society

The theory of complex dynamics, whose roots lie in 19th-century studies of
the iteration of complex function conducted by Kœnigs, Schröder, and
others, flourished remarkably during the first half of the 20th century,
when many of the central ideas and techniques of the subject developed.
This book by Alexander, Iavernaro, and Rosa paints a robust picture of the
field of complex dynamics between 1906 and 1942 through detailed
discussions of the work of Fatou, Julia, Siegel, and several others.

A recurrent theme of the authors' treatment is the center problem
in complex dynamics. They present its complete history during this
period and, in so doing, bring out analogies between complex dynamics
and the study of differential equations, in particular, the problem of
stability in Hamiltonian systems. Among these analogies are the use of
iteration and problems involving small divisors which the authors
examine in the work of Poincaré and others, linking them to
complex dynamics, principally via the work of Samuel Lattès, in the
early 1900s, and Jürgen Moser, in the 1960s.

Many details will be new to the reader, such as a history of Lattès
functions (functions whose Julia set equals the Riemann sphere), complex
dynamics in the United States around the time of World War I, a survey of
complex dynamics around the world in the 1920s and 1930s, a discussion of
the dynamical programs of Fatou and Julia during the 1920s, and
biographical material on several key figures. The book contains graphical
renderings of many of the mathematical objects the authors discuss,
including some of the intriguing fractals Fatou and Julia studied, and
concludes with several appendices by current researchers in complex
dynamics which collectively attest to the impact of the work of Fatou,
Julia, and others upon the present-day study.

#### Table of Contents

# Table of Contents

## Early Days in Complex Dynamics: A history of complex dynamics in one variable during 1906-1942

#### Readership

Graduate students and research mathematicians interested in complex dynamics, complex analysis, and the history of mathematics.