Nonlinear Perron–Frobenius Theory

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  • Format: Hardcover
  • Copyright: 2012-06-29
  • Publisher: Cambridge University Press
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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.

Table of Contents

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
The Birkhoff-Hopf theorem
Classical Perron-Frobenius theory
Notes and comments
List of symbols
Table of Contents provided by Publisher. All Rights Reserved.

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