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Generalizations of the Perron-Frobenius Theorem for Nonlinear Maps
R. D. Nussbaum, Rutgers University, Piscataway, NJ, and S. M. Verduyn Lunel, Vrije University, Amsterdam, Netherlands
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Memoirs of the American Mathematical Society
1999; 98 pp; softcover
Volume: 138
ISBN-10: 0-8218-0969-5
ISBN-13: 978-0-8218-0969-3
List Price: US$49
Individual Members: US$29.40
Institutional Members: US$39.20
Order Code: MEMO/138/659
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The classical Frobenius-Perron Theorem establishes the existence of periodic points of certain linear maps in \({\mathbb R}^n\). The authors present generalizations of this theorem to nonlinear maps.

Readership

Graduate students and research mathematicians working in operator theory.

Table of Contents

  • Introduction
  • Basic properties of admissible arrays
  • Further properties of admissible arrays
  • Computation of the sets \(P(n)\)
  • Necessary conditions for array admissible sets
  • Proof of Theorem C
  • \(P(n)\ne Q(n)\) for general \(n\)
  • \(P_2(n)\) satisfies rule A and rule B
  • The case of linear maps
  • Bibliography
  • Appendix A Description of the program
  • Appendix B Numerical data
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