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Generalizations of the Perron-Frobenius theorem for nonlinear maps

About this Title

R. D. Nussbaum and S. M. Verduyn Lunel

Publication: Memoirs of the American Mathematical Society
Publication Year: 1999; Volume 138, Number 659
ISBNs: 978-0-8218-0969-3 (print); 978-1-4704-0248-8 (online)
DOI: https://doi.org/10.1090/memo/0659
MathSciNet review: 1470912
MSC: Primary 58F20; Secondary 47H99

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Table of Contents

Chapters

  • 1. Introduction
  • 2. Basic properties of admissible arrays
  • 3. More properties of admissible arrays
  • 4. Computation of the sets $P(n)$
  • 5. Necessary conditions for array admissible sets
  • 6. Proof of Theorem C
  • 7. $P(n) \neq Q(n)$ for general $n$
  • 8. $P_2(n)$ satisfies rule A and rule B
  • 9. The case of linear maps