Nonlinear Perron-Frobenius theory /

Nonlinear Perron-Frobenius theory /

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Bibliographic Details
Author / Creator:	Lemmens, Bas.
Imprint:	Cambridge ; New York : Cambridge University Press, 2012.
Description:	xii, 323 p. : ill. ; 24 cm.
Language:	English
Series:	Cambridge tracts in mathematics ; 189 Cambridge tracts in mathematics ; 189.
Subject:	Non-negative matrices. Eigenvalues. Eigenvectors. Algebras, Linear. Algebras, Linear. Eigenvalues. Eigenvectors. Non-negative matrices.
Format:	Print Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/8862516

Hidden Bibliographic Details
Other authors / contributors:	Nussbaum, Roger D., 1944-
ISBN:	9780521898812 (hardback) 0521898811 (hardback)
Notes:	Includes bibliographical references (p. [307]-318) and 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"--

Description
Summary:	In the past several decades the classical Perron-Frobenius theory for nonnegative matrices has been extended to obtain remarkably precise and beautiful results for classes of nonlinear maps. This nonlinear Perron-Frobenius theory has found significant uses in computer science, mathematical biology, game theory and the study of dynamical systems. This is the first comprehensive and unified introduction to nonlinear Perron-Frobenius theory suitable for graduate students and researchers entering the field for the first time. It acquaints the reader with recent developments and provides a guide to challenging open problems. To enhance accessibility, the focus is on finite dimensional nonlinear Perron-Frobenius theory, but pointers are provided to infinite dimensional results. Prerequisites are little more than basic real analysis and topology.
Physical Description:	xii, 323 p. : ill. ; 24 cm.
Bibliography:	Includes bibliographical references (p. [307]-318) and index.
ISBN:	9780521898812 0521898811