One-parameter families of circle diffeomorphisms with strictly monotone rotation number

Kiran Parkhe

We show that if $f:S^1\times S^1\to S^1\times S^1$ is $C^2$, with $f(x,t)=(f_t(x),t)$, and the rotation number of $f_t$ is equal to $t$ for all $t\in S^1$, then $f$…