UID:
almafu_9959245781502883
Format:
1 online resource (xii, 323 pages) :
,
digital, PDF file(s).
Edition:
1st ed.
ISBN:
1-107-22634-1
,
1-280-87795-2
,
9786613719263
,
1-139-37825-2
,
1-139-02607-0
,
1-139-37539-3
,
1-139-37140-1
,
1-139-37968-2
,
1-139-37682-9
Series Statement:
Cambridge tracts in mathematics ; 189
Content:
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.
Note:
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.
,
English
Additional Edition:
ISBN 0-521-89881-1
Language:
English
URL:
https://doi.org/10.1017/CBO9781139026079
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