Rotation rates for a linear flow on a vector bundle

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.