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Dec 26, 2018 at 20:47 comment added Linas What do you mean by "flow"? Do you want a new space, $Y^k=\{(x_t)_{t\in\mathbb{R}} : x_t\in I^k\}$? And why should a (single) $p$-periodic sequence be invariant under $\phi_t$? Yes, certain sets of $p$-periodic sequences might be invariant under $S$; these would be special cases of a subshift, defined as any subspace of $X$ that is invariant under $S$.
May 4, 2017 at 18:04 answer added YCor timeline score: 9
May 4, 2017 at 16:57 comment added YCor You might write $X^k$ (or $X_k$) instead of $X$, since, as you have pointed out, the dependence on $k$ is important
May 4, 2017 at 16:44 history edited Christian Remling
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May 4, 2017 at 16:35 history asked Christian Remling CC BY-SA 3.0