Description
Book SynopsisIn recent years nonlinear PerronFrobenius 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.
Trade 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
Table of ContentsPreface; 1. What is nonlinear Perron–Frobenius theory?; 2. Non-expansiveness and nonlinear Perron–Frobenius theory; 3. Dynamics of non-expansive maps; 4. Sup-norm non-expansive maps; 5. Eigenvectors and eigenvalues of nonlinear cone maps; 6. Eigenvectors in the interior of the cone; 7. Applications to matrix scaling problems; 8. Dynamics of subhomogeneous maps; 9. Dynamics of integral-preserving maps; Appendix A. The Birkhoff–Hopf theorem; Appendix B. Classical Perron–Frobenius theory; Notes and comments; References; List of symbols; Index.
