Polynomial growth of the derivative for diffeomorphisms on tori
Polynomial growth of the derivative for diffeomorphisms on tori
We consider area--preserving zero entropy ergodic diffeomorphisms on tori. We classify such diffeomorphisms for which the sequence {$Df^n$} has a polynomial growth on the $3$-torus: they are necessary of the form <p align="center"> $\mathbb T^3\quad (x_1,x_2,x_3)\mapsto (x_1+\alpha,\varepsilon x_2+\beta(x_1),x_3+\gamma(x_1,x_2))\in\mathbb T^3, <p align="left" class="times"> where $\varepsilon =\pm 1$. We also indicate why …