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Nonlinear Perron-Frobenius theory

Lemmens, Bas.

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Nonlinear Perron-Frobenius theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Nonlinear Perron-Frobenius theory/ Bas Lemmens, Roger Nussbaum.
Author:	Lemmens, Bas.
other author:	Nussbaum, Roger D.,
Published:	Cambridge :Cambridge University Press, : 2012.,
Description:	xii, 323 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
[NT 15003449]:	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.
Subject:	Non-negative matrices. -
Online resource:	https://doi.org/10.1017/CBO9781139026079
ISBN:	9781139026079

Nonlinear Perron-Frobenius theory
Lemmens, Bas.

Nonlinear Perron-Frobenius theory[electronic resource] /Bas Lemmens, Roger Nussbaum. - Cambridge :Cambridge University Press,2012. - xii, 323 p. :ill., digital ;24 cm. - 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.

ISBN: 9781139026079Subjects--Topical Terms:

646556
Non-negative matrices.

LC Class. No.: QA188 / .L456 2012

Dewey Class. No.: 512.5

Nonlinear Perron-Frobenius theory
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245 1 0 $a Nonlinear Perron-Frobenius theory $h [electronic resource] / $c Bas Lemmens, Roger Nussbaum.
260 $a Cambridge : $b Cambridge University Press, $c 2012.
300 $a xii, 323 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge tracts in mathematics ; $v 189
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a 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.
520 $a 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.
650 0 $a Non-negative matrices. $3 646556
650 0 $a Eigenvalues. $3 631789
650 0 $a Eigenvectors. $3 836550
650 0 $a Algebras, Linear. $3 521915
700 1 $a Nussbaum, Roger D., $d 1944- $3 2012775
830 0 $a Cambridge tracts in mathematics ; $v 189. $3 3470480
856 4 0 $u https://doi.org/10.1017/CBO9781139026079