Smooth times of a flow in dimension $1$
Smooth times of a flow in dimension $1$
Let $\alpha$ be an irrational number and $I$ an interval of $\mathbb{R}$. If $\alpha$ is diophantine, we show that any one-parameter group of homeomorphisms of $I$ whose time-$1$ and $\alpha$ maps are $C^\infty$ is in fact the flow of a $C^\infty$ vector field. If $\alpha$ is Liouville on the other …