Cambridge ; New York : Cambridge University Press, 2012.
Format:
Book
xii, 323 p. : ill ; 24 cm.
Bibliography:
Includes bibliographical references (p. [307]-318) and index.
Contents:
Machine generated contents note: Preface; 1. What is nonlinear Perron-Frobenius theory?; 2. Non-expansiveness and nonlinear Perron-Frobenius theory; 3. Dynamics of non-expansive maps; 4. Sup-norm non-expansive 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 integral-preserving maps; Appendix A. The Birkhoff-Hopf theorem; Appendix B. Classical Perron-Frobenius theory; References; Index.
Summary:
"Sometimes in mathematics an innocent-looking 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 Perron-Frobenius theory"-- Provided by publisher.