Polynomial growth of the derivative for diffeomorphisms on tori
| dc.creator | Fraczek, Krzysztof | |
| dc.date | 2002-05-06 | |
| dc.date.accessioned | 2026-07-07T04:48:16Z | |
| dc.date.available | 2026-07-07T04:48:16Z | |
| dc.description | We consider area--preserving diffeomorphisms on tori with zero entropy. We classify ergodic area--preserving diffeomorphisms of the 3--torus for which the sequence $\{Df^n\}_{n\in{\Bbb N}}$ has polynomial growth. Roughly speaking, the main theorem says that every ergodic area--preserving $C^2$--diffeomorphism with polynomial uniform growth of the derivative is $C^2$--conjugate to a 2--steps skew product of the form \[\tor^3\ni(x_1,x_2,x_3)\mapsto (x_1+α,\ep x_2+β(x_1),x_3+γ(x_1,x_2))\in\tor^3,\] where $\ep=\pm 1$. We also indicate why there is no 4--dimensional analogue of the above result. Random diffeomorphisms on the 2--torus are studied as well. | |
| dc.description | 41 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0205044 | |
| dc.identifier | http://arxiv.org/abs/math/0205044 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63981 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37A05, 37C05, 37C40 | |
| dc.title | Polynomial growth of the derivative for diffeomorphisms on tori | |
| dc.type | text |