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Generalizations of the Perron-Frobenius Theorem for Nonlinear Maps
 
R. D. Nussbaum Rutgers University, Piscataway, NJ
S. M. Verduyn Lunel Vrije University, Amsterdam, Netherlands
Generalizations of the Perron-Frobenius Theorem for Nonlinear Maps
eBook ISBN:  978-1-4704-0248-8
Product Code:  MEMO/138/659.E
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $29.40
Generalizations of the Perron-Frobenius Theorem for Nonlinear Maps
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Generalizations of the Perron-Frobenius Theorem for Nonlinear Maps
R. D. Nussbaum Rutgers University, Piscataway, NJ
S. M. Verduyn Lunel Vrije University, Amsterdam, Netherlands
eBook ISBN:  978-1-4704-0248-8
Product Code:  MEMO/138/659.E
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $29.40
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1381999; 98 pp
    MSC: Primary 47

    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
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1381999; 98 pp
MSC: Primary 47

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.

  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.