Minimal Homeomorphisms on Low-Dimension Tori
| dc.creator | Santos, N. M. Dos | |
| dc.creator | UrzÚa-Luz, R. | |
| dc.date | 2007-11-06 | |
| dc.date.accessioned | 2026-07-07T08:41:16Z | |
| dc.date.available | 2026-07-07T08:41:16Z | |
| dc.description | In this article we study minimal homeomorphisms(all orbits are dense) of the tori $T^{n},$ $n<5.$ The linear part of a homeomorphism $ϕ$ of $T^{n}$ is the linear mapping $L$ induced by $ϕ$ on the first homology group of $T^{n}$. It follows from the Lefschetz fixed point theorem that 1 is an eigenvalue of $L$ if $ϕ$ minimal. We show that if $ϕ$ is minimal and $n<5$ then $L$ is quasi-unipontent, i.e., all the eigenvalues of $L$ are roots of unity and conversely if $L\in GL(n,\Z)$ is quasi-unipotent and 1 is an eigenvalue of $L$ then there exists a $ C^{\infty}$ minimal skew-product diffeomorphism $ϕ$ of $T^{n}$ whose linear part is precisely $L.$ We do not know if these results are true for $n>4$. We give a sufficient condition for a smooth skew-product diffeomorphism of a torus of arbitrary dimension to be smoothly conjugate to an affine transformation. | |
| dc.description | 16 PAGES | |
| dc.identifier | https://arxiv.org/abs/0711.0979 | |
| dc.identifier | http://arxiv.org/abs/0711.0979 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141628 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37B05, 37C05, 57E05, 54H20 | |
| dc.title | Minimal Homeomorphisms on Low-Dimension Tori | |
| dc.type | text |