Nonlinear Perron-Frobenius theory / Bas Lemmens, Roger Nussbaum.Material type: TextSeries: Cambridge tracts in mathematics ; 189.Publication details: Cambridge : Cambridge University Press, 2012. Description: 1 online resource (xii, 323 pages) : illustrations, tablesContent type: text Media type: computer Carrier type: online resourceISBN: 9781139026079; 1139026070; 9780521898812; 0521898811; 1280877952; 9781280877957; 9781139376822; 1139376829; 9781139379687; 1139379682; 9781139375399; 1139375393; 1107226341; 9781107226340; 9786613719263; 6613719269; 1139378252; 9781139378253; 1139371401; 9781139371407Subject(s): Non-negative matrices | Eigenvalues | Eigenvectors | Algebras, Linear | MATHEMATICS -- Differential Equations | MATHEMATICS -- Algebra -- Linear | Algebras, Linear | Eigenvalues | Eigenvectors | Non-negative matricesGenre/Form: Electronic book. | Electronic books. | Electronic books. Additional physical formats: Print version:: No titleDDC classification: 512.5 | 512/.5 LOC classification: QA188 .L456 2012Other classification: MAT007000 Online resources: Click here to access online
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Title from publishers bibliographic system (viewed 09 May 2012).
Includes chapter notes and comments, bibliographical references (pages 307-318), list of symbols, and index.
880-01 Cover; CAMBRIDGE TRACTS IN MATHEMATICS; GENERAL EDITORS; Title; Copyright; Contents; Preface; 1 What is nonlinear Perron-Frobenius theory?; 1.1 Classical Perron-Frobenius theory; 1.2 Cones and partial orderings; 1.3 Order-preserving maps; 1.4 Subhomogeneous maps; 1.5 Topical maps; 1.6 Integral-preserving maps; 2 Non-expansiveness and nonlinear Perron-Frobenius theory; 2.1 Hilbert's and Thompson's metrics; 2.2 Polyhedral cones; 2.3 Lorentz cones; 2.4 The cone of positive-semidefinite symmetric matrices; 2.5 Completeness; 2.6 Convexity and geodesics; 2.7 Topical maps and the sup-norm.
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.