Nonlinear Perron-Frobenius theory /
Lemmens, Bas,
Nonlinear Perron-Frobenius theory / Bas Lemmens, Roger Nussbaum. - Cambridge : Cambridge University Press, 2012. - 1 online resource (xii, 323 pages) : digital, PDF file(s). - Cambridge tracts in mathematics ; 189 . - Cambridge tracts in mathematics ; 189. .
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.
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.
9781139026079 (ebook)
Non-negative matrices.
Eigenvalues.
Eigenvectors.
Algebras, Linear.
QA188 / .L456 2012
512/.5
Nonlinear Perron-Frobenius theory / Bas Lemmens, Roger Nussbaum. - Cambridge : Cambridge University Press, 2012. - 1 online resource (xii, 323 pages) : digital, PDF file(s). - Cambridge tracts in mathematics ; 189 . - Cambridge tracts in mathematics ; 189. .
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.
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.
9781139026079 (ebook)
Non-negative matrices.
Eigenvalues.
Eigenvectors.
Algebras, Linear.
QA188 / .L456 2012
512/.5