Nonlinear Perron–Frobenius Theory: 189 (Cambridge Tracts in Mathematics, Series Number 189)
Cambridge University Press
Edition: Illustrated, 5/3/2012
EAN 9780521898812, ISBN10: 0521898811
Hardcover, 336 pages, 23.4 x 15.5 x 2 cm
Language: English
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.
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.
'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