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Topologically Transitive Flow on $R^n$

Mathematics Asked on December 27, 2021

I have been looking but cannot find the following: an example of a topologically transitive map on $mathbb{S}^n$ or on $mathbb{R}^n$ (for arbitrary $n$). Here, by a topologically transitive flow, I mean a smooth map
$$
begin{aligned}
f:[0,1]times mathbb{S}^n rightarrow mathbb{S}^n
end{aligned}
$$

such that ${f(t,x):t in [0,1]}$ is dense in $mathbb{S}^n$ for some $x in mathbb{S}^n$.

One Answer

Answered by John B on December 27, 2021

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