The story of the development of complex dynamics over the first half of the 20th century begins by introducing the origins of the field in the 19th century. Then it moves to differential equations, with an emphasis on the relation of Henri Poincaré to the study of complex dynamics and the problem of small divisors. The center of the history, of course, focuses on the work of Pierre Fatou and Gaston Julia, but the narrative extends beyond them through the beginnings of transcendental and algebraic dynamics to the center problem and Carl Ludwig Siegal solution of it in 1942. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)