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Zusatztext '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 Informationen zum Autor 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. Klappentext Guides the reader through the nonlinear Perron-Frobenius theory, introducing them to recent developments and challenging open problems. Zusammenfassung 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. Inhaltsverzeichnis Preface; 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.
