A uniform exponential spectrum for linear flows on vector bundles
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.
scientific article; zbMATH DE number 1547254