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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
Available Formats:
Electronic 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 Click above image for expanded view Generalizations of the Perron-Frobenius Theorem for Nonlinear Maps R. D. Nussbaum Rutgers University, Piscataway, NJ S. M. Verduyn Lunel Vrije University, Amsterdam, Netherlands Available Formats:  Electronic 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.

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
• Requests

Review Copy – for reviewers who would like to review an AMS book
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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.

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 reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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