Nonlinear Perron–Frobenius Theory: 189 (Cambridge Tracts in Mathematics, Series Number 189) - Hardcover

Lemmens, Bas; Nussbaum, Roger

Hardcover

ISBN 10: 0521898811 ISBN 13: 9780521898812

Publisher: Cambridge University Press, 2012

Synopsis

In the past several decades the classical Perron–Frobenius theory for nonnegative matrices has been extended to obtain remarkably precise and beautiful results for classes of nonlinear maps. This nonlinear Perron–Frobenius theory has found significant uses in computer science, mathematical biology, game theory and the study of dynamical systems. This is the first comprehensive and unified introduction to nonlinear Perron–Frobenius theory suitable for graduate students and researchers entering the field for the first time. It acquaints the reader with recent developments and provides a guide to challenging open problems. To enhance accessibility, the focus is on finite dimensional nonlinear Perron–Frobenius theory, but pointers are provided to infinite dimensional results. Prerequisites are little more than basic real analysis and topology.

About this title

Review:

'In their introduction the authors state that 'the main purpose of this book is to give a systematic self-contained introduction to nonlinear Perron–Frobenius theory and to provide a guide to various challenging open problems'. They have achieved their aim excellently.' Hans Schneider, University of Wisconsin, Madison

'Undoubtedly, this remarkable book will be of interest to all specialists in nonlinear analysis and its applications. Certainly, any mathematical library ought to carry this book.' Peter Zabreiko, Zentralblatt MATH

'This textbook is a carefully arranged journey through large parts of this beautiful theory, which has seen various contributions by the authors in the past. The material is accessible with little more than a basic knowledge of linear algebra, real analysis and some topology. The book is self-contained, all results are proven very rigorously, and where appropriate, the evolution of results is explained and framed in the historical context. I recommend this book very warmly and without any reservations to anyone interested in nonlinear Perron–Frobenius theory.' Bjorn S. Ruffer, Mathematical Reviews

Book Description:

In recent years nonlinear Perron–Frobenius theory has grown into a beautiful subject with significant applications. This self-contained introduction to the topic is suitable for graduate students and researchers entering the field for the first time and provides a guide to challenging open problems.

About this edition

• Publisher: Cambridge University Press
• Publication date: 2012
• ISBN 10: 0521898811
• ISBN 13: 9780521898812
• Binding: Hardcover
• Number of pages: 336