Given a section of the flow $\Phi^t(x_0)$ (for finite $t$), I'd like to denote a subsection of this flow from times $\tau^{i-1}$ to time $\tau^{i}$ using similar notation.
I was considering using something like: $\phi_i = \Phi^\tau(\Phi^{\tau^{i-1}}(x_0)), \forall\tau\in[\tau^{i-1},\tau^{i}]$
However I thought that this seemed a bit hacky, and sadly after much searching online I've not found anything more beautiful or concise.
If you need more details on my motivation behind wanting to do this before you can advise me, then I'll gladly update my post with such information.
Thanks in advance!