Early Days in Complex Dynamics


Book Description

The theory of complex dynamics, whose roots lie in 19th-century studies of the iteration of complex function conducted by Koenigs, Schoder, 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 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 History of Complex Dynamics


Book Description

The contemporary study of complex dynamics, which has flourished so much in recent years, is based largely upon work by G. Julia (1918) and P. Fatou (1919/20). The goal of this book is to analyze this work from an historical perspective and show in detail, how it grew out of a corpus regarding the iteration of complex analytic functions. This began with investigations by E. Schröder (1870/71) which he made, when he studied Newton's method. In the 1880's, Gabriel Koenigs fashioned this study into a rigorous body of work and, thereby, influenced a lot the subsequent development. But only, when Fatou and Julia applied set theory as well as Paul Montel's theory of normal families, it was possible to develop a global approach to the iteration of rational maps. This book shows, how this intriguing piece of modern mathematics became reality.




Revision of Sternaspis Otto, 1821 (Polychaeta, Sternaspidae)


Book Description

The peanut-shaped sternaspid polychaetes have been known since 1760 when Plancus named them as Mentula cucurbitacea marina. Sternaspids are common and abundant in soft bottoms. Some authors suggested that only one species should be recognized, whereas others regard a few species very widely distributed and variable depths. Delineating species was problematic; the ventro-caudal shield was disregarded or barely used for identifying species. In this contribution the ventral shield is evaluated and its diagnostic potential is confirmed. The revision of Sternaspis is based upon type or topotype materials. Sternaspid body, introvert hooks and shield show three distinct patterns: two genera have 7 abdominal segments and tapered introvert hooks, and one genus has 8 abdominal segments and spatulate introvert hooks. The ventro-caudal shield has 3 different patterns: stiff with ribs, and sometimes concentric lines, stiff with feebly-defined ribs but no concentric lines, and soft with firmly adhered sediment particles. Sternaspis is restricted to include species with 7 abdominal segments, falcate introvert hooks, and stiff shields, often exhibiting radial ribs, concentric lines or both. Two new genera incorporate the remaining species: Caulleryaspis has falcate introvert hooks, 7 abdominal segments, and soft shields with sediment particles firmly adhered on them. Petersenaspis has spatulate introvert hooks, 8 abdominal segments, and stiff shields with poorly-defined ribs but no concentric line. The geographic range of most species is smaller than previously indicated. Keys to genera and to all species are also included.




The Taming of Chance


Book Description

This book combines detailed scientific historical research with characteristic philosophic breadth and verve.




Margaret of York, Simon Marmion, and The Visions of Tondal


Book Description

Presented at a symposium held in 1990 to celebrate the Getty Museum's acquisition of the only known illuminated copy of The Visions of Tondal, twenty essays address the celebrated bibliophilic activity of Margaret of York; the career of Simon Marmion, a favorite artist of the Burgundian court; and The Visions of Tondal in relation to illustrated visions of the Middle Ages. Contributors include Maryan Ainsworth, Wim Blockmans, Walter Cahn, Albert Derolez, Peter Dinzelbacher, Rainald Grosshans, Sandra Hindman, Martin Lowry, Nigel Morgan, and Nigel Palmer.