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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!

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    $\begingroup$ I also haven't seen any notation for this, but I'd probably prefer $\phi_i = \{\Phi^t(x_0)\ |\ \tau^{i-1}\leq t\leq \tau^i\}$. $\endgroup$ – Mankind Mar 30 '15 at 13:25
  • $\begingroup$ I was really surprised that there's no standard notation for this, but I guess that's just because I often deal with numerical approximations of dynamical systems, which this notation wasn't necessarily made for. Thanks so much for your input, I really appreciate it! $\endgroup$ – Daniel Crane Mar 30 '15 at 13:29

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