Lyapunov, metric and flag spectra

TL;DR

This paper introduces the metric spectrum to quantify approximation rates near invariant sets and relates it to Lyapunov spectra, providing explicit calculations for Morse components on flag manifolds.

Contribution

It defines the metric spectrum and connects it to Lyapunov spectra, with explicit results for Morse components on generalized flag manifolds.

Findings

Metric spectrum measures exponential approximation rates.

Explicit metric spectrum for Morse components on flag manifolds.

Relation established between metric and Lyapunov spectra.

Abstract

We introduce the \emph{metric spectrum}, which measures the exponential rate of approximation to an isolated invariant set of points starting in its stable set, and relate it to the Lyapunov spectrum. We determine the metric spectrum of each Morse component of the finest Morse decomposition of a linear induced flow on a generalized flag manifold.