Birkhoff's version of Hilbert's metric and its applications in analysis

TL;DR

This survey explores the applications of Birkhoff's version of Hilbert's metric in analyzing the behavior of linear and nonlinear mappings on cones, highlighting its significance in Hilbert geometry.

Contribution

It provides a comprehensive overview of how Birkhoff's Hilbert metric is utilized in analysis and dynamics within cone structures, consolidating existing knowledge.

Findings

Summarizes key applications in linear and nonlinear analysis

Highlights the role of Hilbert's metric in dynamics of cone mappings

Provides insights into geometric properties relevant to analysis

Abstract

This is a survey article concerning applications of Hilbert's metric in the analysis and dynamics of linear and nonlinear mappings on cones. It will appear as a chapter in the "Handbook of Hilbert geometry", ed. G. Besson, A. Papadopoulos and M. Troyanov, European Mathematical Society Publishing House, Z\"urich.