Nonlinear PerronFrobenius theory
 Author/Creator
 Lemmens, Bas.
 Language
 English.
 Imprint
 Cambridge ; New York : Cambridge University Press, 2012.
 Physical description
 xii, 323 p. : ill ; 24 cm.
 Series
 Cambridge tracts in mathematics ; 189.
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Contributors
 Contributor
 Nussbaum, Roger D., 1944
Contents/Summary
 Bibliography
 Includes bibliographical references (p. [307]318) and index.
 Contents

 Machine generated contents note: Preface; 1. What is nonlinear PerronFrobenius theory?; 2. Nonexpansiveness and nonlinear PerronFrobenius theory; 3. Dynamics of nonexpansive maps; 4. Supnorm nonexpansive maps; 5. Eigenvectors and eigenvalues of nonlinear cone maps; 6. Eigenvectors in the interior of the cone; 7. Applications to matrix scaling problems; 8. Dynamics of subhomogeneous maps; 9. Dynamics of integralpreserving maps; Appendix A. The BirkhoffHopf theorem; Appendix B. Classical PerronFrobenius theory; References; Index.
 Summary
 "Sometimes in mathematics an innocentlooking observation opens up a new road to a fertile field. A nice example of such an observation is due to Garrett Birkhoff [23] and Hans Samelson [187], who remarked that one can use Hilbert's (projective) metric and the contraction mapping principle to prove some of the theorems of Perron and Frobenius concerning eigenvectors and eigenvalues of nonnegative matrices. This idea has been pivotal for the development of nonlinear PerronFrobenius theory" Provided by publisher.
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Bibliographic information
 Publication date
 2012
 Responsibility
 Bas Lemmens, Roger Nussbaum.
 Series
 Cambridge tracts in mathematics ; 189
 ISBN
 9780521898812
 0521898811