Nonlinear Perron-Frobenius theory
- Bas Lemmens, Roger Nussbaum.
- Cambridge ; New York : Cambridge University Press, 2012.
- Physical description
- xii, 323 p. : ill ; 24 cm.
- Cambridge tracts in mathematics ; 189.
Math & Statistics Library
QA188 .L456 2012
- Unknown QA188 .L456 2012
- Includes bibliographical references (p. -318) and index.
- 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.
- (source: Nielsen Book Data)
- Publisher's Summary
- 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.
(source: Nielsen Book Data)
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- Publication date
- Cambridge tracts in mathematics ; 189
- 9780521898812 (hardback)
- 0521898811 (hardback)