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200 10$aNonlinear Perron-Frobenius theory /$fBas Lemmens, Roger Nussbaum$b[electronic resource]
210  1$aCambridge :$cCambridge University Press,$d2012.
215   $a1 online resource (xii, 323 pages) $cdigital, PDF file(s)
225 1 $aCambridge tracts in mathematics ;$v189
300   $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
311   $a0-521-89881-1 
320   $aIncludes bibliographical references (p. [307]-318) and index.
327   $aPreface -- 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.
330   $aIn the past several decades the classical Perron-Frobenius theory for nonnegative matrices has been extended to obtain remarkably precise and beautiful results for classes of nonlinear maps. This nonlinear Perron-Frobenius theory has found significant uses in computer science, mathematical biology, game theory and the study of dynamical systems. This is the first comprehensive and unified introduction to nonlinear Perron-Frobenius theory suitable for graduate students and researchers entering the field for the first time. It acquaints the reader with recent developments and provides a guide to challenging open problems. To enhance accessibility, the focus is on finite dimensional nonlinear Perron-Frobenius theory, but pointers are provided to infinite dimensional results. Prerequisites are little more than basic real analysis and topology.
410  0$aCambridge tracts in mathematics ;$v189.
606   $aNon-negative matrices
606   $aEigenvalues
606   $aEigenvectors
606   $aAlgebras, Linear
615  0$aNon-negative matrices.
615  0$aEigenvalues.
615  0$aEigenvectors.
615  0$aAlgebras, Linear.
676   $a512/.5
686   $aMAT007000$2bisacsh
700   $aLemmens$b Bas$0516851
702   $aNussbaum$b Roger D.$f1944-
801  0$bUkCbUP
801  1$bUkCbUP
906   $aBOOK
912   $a9910809659603321
996   $aNonlinear Perron-Frobenius theory$94116889
997   $aUNINA