A Multiplicative Ergodic Theorem and Nonpositively Curved Spaces View Full Text


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Article Info

DATE

1999-12

AUTHORS

Anders Karlsson, Gregory A. Margulis

ABSTRACT

We study integrable cocycles u(n,x) over an ergodic measure preserving transformation that take values in a semigroup of nonexpanding maps of a nonpositively curved space Y, e.g. a Cartan–Hadamard space or a uniformly convex Banach space. It is proved that for any y∈Y and almost all x, there exist A≥ 0 and a unique geodesic ray γ (t,x) in Y starting at y such that\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} In the case where Y is the symmetric space GLN(ℝ)/ON(ℝ) and the cocycles take values in GLN(ℝ), this is equivalent to the multiplicative ergodic theorem of Oseledec. Two applications are also described. The first concerns the determination of Poisson boundaries and the second concerns Hilbert-Schmidt operators. More... »

PAGES

107-123

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s002200050750

DOI

http://dx.doi.org/10.1007/s002200050750

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1000583770


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