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
- computer
- online resource
- 9781139026079
- 1139026070
- 9780521898812
- 0521898811
- 1280877952
- 9781280877957
- 9781139376822
- 1139376829
- 9781139379687
- 1139379682
- 9781139375399
- 1139375393
- 1107226341
- 9781107226340
- 9786613719263
- 6613719269
- 1139378252
- 9781139378253
- 1139371401
- 9781139371407
- 512.5 512/.5
- QA188 .L456 2012
- MAT007000
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Electronic-Books | OPJGU Sonepat- Campus | E-Books EBSCO | Available |
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.
English.
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