TY  - BOOK
AU  - Lemmens,Bas
AU  - Nussbaum,Roger D.
TI  - Nonlinear Perron-Frobenius theory
T2  - Cambridge tracts in mathematics
SN  - 9781139026079 (ebook)
AV  - QA188 .L456 2012
U1  - 512/.5 23
PY  - 2012///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Non-negative matrices
KW  - Eigenvalues
KW  - Eigenvectors
KW  - Algebras, Linear
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015); Preface -- What is nonlinear Perron-Frobenius theory? -- Non-expansiveness and nonlinear Perron-Frobenius theory -- Dynamics of non-expansive maps -- Sup-norm non-expansive maps -- Eigenvectors and eigenvalues of nonlinear cone maps -- Eigenvectors in the interior of the cone -- Applications to matrix scaling problems -- Dynamics of subhomogeneous maps -- Dynamics of integral-preserving maps -- Appendix A. The Birkhoff-Hopf theorem -- Appendix B. Classical Perron-Frobenius theory
N2  - 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
UR  - https://doi.org/10.1017/CBO9781139026079
ER  -