The Real Fatou Conjecture - Couverture souple

Graczyk, Jacek

Couverture souple

ISBN 10 : 0691002584 ISBN 13 : 9780691002583

Editeur : Princeton University Press, 1998

Synopsis

In 1920, Pierre Fatou expressed the conjecture that-except for special cases-all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration. This conjecture remains the main open problem in the dynamics of iterated maps. For the logistic family x- ax(1-x), it can be interpreted to mean that for a dense set of parameters "a" an attracting periodic orbit exists. The same question appears naturally in science, where the logistic family is used to construct models in physics, ecology, and economics. In this book, Jacek Graczyk and Grzegorz Swiatek provide a rigorous proof of the Real Fatou Conjecture. In spite of the apparently elementary nature of the problem, its solution requires advanced tools of complex analysis. The authors have written a self-contained and complete version of the argument, accessible to someone with no knowledge of complex dynamics and only basic familiarity with interval maps. The book will thus be useful to specialists in real dynamics as well as to graduate students.

A propos du livre

À propos de l?auteur

Jacek Graczyk is Assistant Professor of Mathematics at Michigan State University. Grzegorz Swiatek is Associate Professor of Mathematics at Pennsylvania State University.

Détails de l'édition

• Éditeur: Princeton University Press
• Date d'édition: 1998
• Langue: anglais
• ISBN 10: 0691002584
• ISBN 13: 9780691002583
• Reliure: Broché
• Nombre de pages: 158
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible