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Recurrent dimensions of quasi-periodic solutions for nonlinear evolution equations II: Gaps of dimensions and Diophantine conditions
Polynomial growth of the derivative for diffeomorphisms on tori
| 1. | Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland |
$\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,
where $\varepsilon =\pm 1$. We also indicate why there is no $4$-dimensional analogue of the above result. Random diffeomorphisms on the $2$-torus are studied as well.
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