A uniform exponential spectrum for linear flows on vector bundles
type: Item
instance of: scholarly article
title: A uniform exponential spectrum for linear flows on vector bundles
zbMATH Open document ID: 0983.37032
DOI: 10.1023/A:1009024610394
author: Lars Grüne
published in: Journal of Dynamics and Differential Equations
publication date: 2001-03-12T00:00:00Z
review text: It is known that spectral concepts for linear flows \(\varphi: \mathbb{R} \times E\to E\) on vector bundles \(\pi:E\to S\) with compact base space \(S\) can roughly be divided into two classes: one using exponential growth rates and the other using topological characterizations of the flow projected onto the projective bundle. Here the author introduces a spectral concept that lies somewhat in between these approaches. He considers the set of all possible exponential growth rates in some finite time \(T>0\) with initial values in this set and defines the spectrum to consist of all accumulation points as \(T\to \infty\). He proves that for a connected compact invariant set this spectrum is a closed interval whose boundary points are Lyapunov exponents.
Mathematics Subject Classification ID: 37D25
Mathematics Subject Classification ID: 34D08
Mathematics Subject Classification ID: 37C35
zbMATH DE Number: 1547254
zbMATH Keywords: linear flow
zbMATH Keywords: uniform
zbMATH Keywords: exponential spectrum
zbMATH Keywords: Lyapunov exponent
zbMATH Keywords: accumulation point
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: a:1009024610394
OpenAlex ID: W170618279
description: scientific article; zbMATH DE number 1547254