Eigenvalues of transformations arising from irrational rotations and step functions. (Valeurs propres de transformations liées aux rotations irrationnelles et aux fonctions en escalier)
| dc.creator | Guenais, Melanie | |
| dc.creator | Parreau, Francois | |
| dc.date | 2006-05-10 | |
| dc.date.accessioned | 2026-07-07T07:39:41Z | |
| dc.date.available | 2026-07-07T07:39:41Z | |
| dc.description | Given an irrational rotation $T$ on $\M T$ we settle necessary and sufficient conditions on a step function $ϕ$ and $t\in \M T$ for the existence of measurable solutions to the cohomogical equation $$\exp{(2iπϕ)}=\e{2iπt}f/f\rond T.$$ This yields a characterization of eigenvalues and eigenfunctions for several transformations arising from irrational rotations and step functions: cylinder flows, special flows, induced maps... From there we give constructions of special flows and three-interval exchange transformations with unusual spectral properties. In both cases we exhibit examples with Kronecker factors of infinite rank. We also construct three-interval exchange transformations which are non-trivially conjugate to irrational rotations or to odometers. Similarly there exist special flows over irrational rotations which are non-trivially conjugate to translations flows on $\M T^2$ or on solenoids. Finally, we prove a regularization property which allows us to give similar examples of special flows with smooth ceiling functions, under natural Diophantine conditions for the rotation. | |
| dc.description | francais, 80 pages | |
| dc.identifier | https://arxiv.org/abs/math/0605250 | |
| dc.identifier | http://arxiv.org/abs/math/0605250 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121542 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 28D10 | |
| dc.title | Eigenvalues of transformations arising from irrational rotations and step functions. (Valeurs propres de transformations liées aux rotations irrationnelles et aux fonctions en escalier) | |
| dc.type | text |