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 $x in mathbb{S}^n$.
You can have a look at the paper
V. López and G. López, Transitive flows on manifolds, Rev. Mat. Iberoam. 20 (2004), 107-130
for the general solution.
Answered by John B on December 27, 2021
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