I am reading a paper by Langerock, called "A connection theoretic approach to sub-Riemannian geometry".
He writes:
[Let $\pi:E\rightarrow M$ be a vector bundle] ... Let $\{\phi_t\}$ represent the flow of the canonical dilation vector field on $E$ i.e. in natural vector bundle cooordinates $(x^i,y^A)$ on $E$ we have $$\phi_t(x^i,y^A)=(x^i,e^ty^A)$$
Now, I searched online but I cannot figure out what a canonical dilation vector field on a vector bundle is. Moreover, I cannot figure out what $e^t$ is in the above notation.
My best guess is that $\phi_t:E\rightarrow E$ maps a point $e=(x^i,y^A)$ to the point obtained letting $e$ act $t$ times on itself (through the action of a vector field on itself, i.e. the one of an abelian group on itself). So we get a vertical action on each fiber when at each $t$ each point $f$ in a generic fiber is sent to $(t+1)f$ in the same fiber.
Am I correct?
Thank in advance