Early Days in Complex Dynamics: A History of Complex Dynamics in One Variable During 1906-1942 (History of Mathematics, 38, Band 38) - Hardcover
Inhaltsangabe
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)
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Über die Autorin bzw. den Autor
Daniel S. Alexander, Drake University, Des Moines, IA, USA
Felice Iavernaro, Università di Bari, Bari, Italy
Alessandro Rosa
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Early Days in Complex Dynamics: A History of Complex Dynamics in One Variable During 1906-1942 (History of Mathematics) (History of Mathematics, 38)
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Zustand: New. Series: History of Mathematics. Num Pages: 442 pages, Illustrations. BIC Classification: PBKS. Category: (G) General (US: Trade). Dimension: 257 x 184 x 29. Weight in Grams: 1000. . 2011. Hardcover. . . . . Bestandsnummer des Verkäufers V9780821844649
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Early Days in Complex Dynamics A history of Complex Dynamics in One Variable during 19061942
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ISBN 10: 0821844644
ISBN 13: 9780821844649
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Hardback. Zustand: New. 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 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 Poincare and others, linking them to complex dynamics, principally via the work of Samuel Lattes, in the early 1900s, and Jurgen Moser, in the 1960s. Many details will be new to the reader, such as a history of Lattes 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. Bestandsnummer des Verkäufers LU-9780821844649
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Early Days in Complex Dynamics: A History of Complex Dynamics in One Variable During 1906-1942 (History of Mathematics)
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Zustand: New. Series: History of Mathematics. Num Pages: 442 pages, Illustrations. BIC Classification: PBKS. Category: (G) General (US: Trade). Dimension: 257 x 184 x 29. Weight in Grams: 1000. . 2011. Hardcover. . . . . Books ship from the US and Ireland. Bestandsnummer des Verkäufers V9780821844649
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Early Days in Complex Dynamics: A history of Complex Dynamics in One Variable during 1906-1942
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American Mathematical Society, 2011
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ISBN 13: 9780821844649
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Early Days in Complex Dynamics
Verlag:
American Mathematical Society, US, 2011
ISBN 10: 0821844644
ISBN 13: 9780821844649
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Hardback. Zustand: New. 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 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 Poincare and others, linking them to complex dynamics, principally via the work of Samuel Lattes, in the early 1900s, and Jurgen Moser, in the 1960s. Many details will be new to the reader, such as a history of Lattes 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. Bestandsnummer des Verkäufers LU-9780821844649
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