Nonlinear Perron-Frobenius theory
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Bibliographic Information
Nonlinear Perron-Frobenius theory
（Cambridge tracts in mathematics, 189）
Cambridge University Press, 2012
Available at / 29 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
Includes bibliographical references (p. [307]-318) and index
Description and Table of Contents
Description
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.
Table of Contents
- 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.
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