The following linear ODE on $\Bbb{C}$
$\dot{z} = (a + i b)z$
has solutions $z(t) = e^{(a+ib)t} z(0)$. Hence the real part $a$ captures expansion rate and the imaginary part $b$ captures rotation rate.
It seems to me that this notion of expansion rate is generalized to a linear flow $\Phi^t$ on a normed vector bundle $\pi:V\to B$ through the notion of Lyapunov exponents $\lambda(v)$ of $v \in V$, where
$$\lambda(v) := \limsup_{t\to\infty}\frac{1}{t}\log |\Phi^tv|.$$
Question: Is it also possible to generalize the "rotation rate" to linear flows on vector bundles? Any explanation/references would be much appreciated.
