Nonlinear Perron–Frobenius Theory

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Bas Lemmens (University of Kent, Canterbury) Roger Nussbaum (Rutgers University, New Jersey)

Nonlinear Perron–Frobenius Theory

Bas Lemmens (University of Kent, Canterbury), Roger Nussbaum (Rutgers University, New Jersey)

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English

Cambridge University Press
03 May 2012

Differential calculus & equations; Integral calculus & equations; Geometry; Topology

Series: Cambridge Tracts in Mathematics

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.

By: Bas Lemmens (University of Kent Canterbury), Roger Nussbaum (Rutgers University, New Jersey)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 189
Dimensions: Height: 234mm, Width: 156mm, Spine: 21mm
Weight: 620g
ISBN: 9780521898812
ISBN 10: 0521898811
Series: Cambridge Tracts in Mathematics
Pages: 336
Publication Date: 03 May 2012
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Bas Lemmens is a Lecturer in Mathematics at the University of Kent, Canterbury. His research interests lie in nonlinear operator theory, dynamical systems theory and metric geometry. He is one of the key developers of nonlinear Perron–Frobenius theory. Roger Nussbaum is a Professor of Mathematics at Rutgers University. His research interests include nonlinear differential-delay equations, the theory of nonlinear positive operators and fixed point theory and its applications. He has published extensively on nonlinear Perron–Frobenius theory.

Reviews for Nonlinear Perron–Frobenius Theory

'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