Nonlinear Perron-Frobenius theory / Bas Lemmens, Roger Nussbaum.

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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,...

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Bibliographic Details
Uniform Title:Cambridge tracts in mathematics ; 189.
Main Authors: Lemmens, Bas (Author)
Nussbaum, Roger D., 1944- (Author)
Language:English
Published: Cambridge : Cambridge University Press, 2012.
Series:Cambridge tracts in mathematics ; 189.
Subjects:
Non-negative matrices.
Eigenvalues.
Eigenvectors.
Algebras, Linear.
Online Access:
Connect to online resource - MSU authorized users (Digital Object Identifier Permalink)
Physical Description:1 online resource (xii, 323 pages) : digital, PDF file(s).
Format: Electronic eBook
Contents:
  • 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.