The "Research Group on Ordered Structures with Applications", which will be held on 07 September 2023 at 2:00 PM CET with the use of the ZOOM platform.
Speaker: Pr. Bas Lemmens, University of Kent, United Kingdom.
Title of the lecture: Nonlinear Perron-Frobenius Theory.
Seminar working language: English.
Abstract: Sometimes in mathematics a simple-looking observation opens up a new road to a fertile field. Such an observation was made independently by Garrett Birkhoff and Hans Samelson, 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.
In the past few decades a number of strikingly detailed nonlinear extensions of Perron–Frobenius theory have been obtained. These results provide an extensive analysis of the eigenvectors and eigenvalues of various classes of order-preserving (monotone) nonlinear maps and give information about their iterative behavior and periodic orbits. They have found applications in computer science, mathematical biology, game theory and the study of dynamical systems.
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