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|a 9781139026079 (ebook)
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|a Lemmens, Bas,
|e author.
|0 http://id.loc.gov/authorities/names/n2012008334
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| 245 |
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|a Nonlinear Perron-Frobenius theory /
|c Bas Lemmens, Roger Nussbaum.
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| 264 |
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|a Cambridge :
|b Cambridge University Press,
|c 2012.
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|a 1 online resource (xii, 323 pages) :
|b digital, PDF file(s).
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|v 189
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|a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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|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.
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|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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| 650 |
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|a Non-negative matrices.
|0 http://id.loc.gov/authorities/subjects/sh85092227
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| 650 |
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|a Eigenvalues.
|0 http://id.loc.gov/authorities/subjects/sh85041389
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| 650 |
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|a Eigenvectors.
|0 http://id.loc.gov/authorities/subjects/sh85041390
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| 650 |
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|a Algebras, Linear.
|0 http://id.loc.gov/authorities/subjects/sh85003441
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| 700 |
1 |
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|a Nussbaum, Roger D.,
|d 1944-
|e author.
|0 http://id.loc.gov/authorities/names/n78044209
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|i Print version:
|a Lemmens, Bas
|t Nonlinear Perron-Frobenius theory
|z 9780521898812.
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|a Cambridge tracts in mathematics ;
|v 189.
|0 http://id.loc.gov/authorities/names/n42005726
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