Nonlinear Perron-Frobenius Theory
Author | : Bas Lemmens |
Publisher | : |
Total Pages | : 323 |
Release | : 2012 |
ISBN-10 | : 1107226341 |
ISBN-13 | : 9781107226340 |
Rating | : 4/5 (41 Downloads) |
Book excerpt: 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.