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Nonlinear Perron-Frobenius theory

Lemmens, Bas.

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Nonlinear Perron-Frobenius theory

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Nonlinear Perron-Frobenius theory/ Bas Lemmens, Roger Nussbaum.
作者:	Lemmens, Bas.
其他作者:	Nussbaum, Roger D.,
出版者:	Cambridge :Cambridge University Press, : 2012.,
面頁冊數:	xii, 323 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
內容註:	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.
標題:	Non-negative matrices. -
電子資源:	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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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.
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