03591nam 22007452 450 991079030530332120151005020624.01-107-22634-11-280-87795-297866137192631-139-37825-21-139-02607-01-139-37539-31-139-37140-11-139-37968-21-139-37682-9(CKB)2670000000207529(EBL)880642(OCoLC)794731490(SSID)ssj0000678523(PQKBManifestationID)11449823(PQKBTitleCode)TC0000678523(PQKBWorkID)10727061(PQKB)11395544(UkCbUP)CR9781139026079(Au-PeEL)EBL880642(CaPaEBR)ebr10574287(CaONFJC)MIL371926(MiAaPQ)EBC880642(PPN)199693226(EXLCZ)99267000000020752920110218d2012|||| uy| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierNonlinear Perron-Frobenius theory /Bas Lemmens, Roger Nussbaum[electronic resource]Cambridge :Cambridge University Press,2012.1 online resource (xii, 323 pages) digital, PDF file(s)Cambridge tracts in mathematics ;189Title from publisher's bibliographic system (viewed on 05 Oct 2015).0-521-89881-1 Includes bibliographical references (p. [307]-318) and index.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.Cambridge tracts in mathematics ;189.Non-negative matricesEigenvaluesEigenvectorsAlgebras, LinearNon-negative matrices.Eigenvalues.Eigenvectors.Algebras, Linear.512/.5MAT007000bisacshLemmens Bas516851Nussbaum Roger D.1944-UkCbUPUkCbUPBOOK9910790305303321Nonlinear Perron-Frobenius theory3823935UNINA