Distortion in Groups of Circle and Surface Diffeomorphisms
| dc.creator | Franks, John | |
| dc.date | 2007-05-28 | |
| dc.date.accessioned | 2026-07-07T08:03:24Z | |
| dc.date.available | 2026-07-07T08:03:24Z | |
| dc.description | In these lectures we consider how algebraic properties of discrete subgroups of Lie groups restrict the possible actions of those groups on surfaces. The results show a strong parallel between the possible actions of such a group on the circle $S^1$ and the measure preserving actions on surfaces. Our aim is the study of the (non)-existence of actions of lattices in a large class of non-compact Lie groups on surfaces. A definitive analysis of the analogous question for actions on $S^1$ was carried out by É. Ghys. Our approach is topological and insofar as possible we try to isolate properties of a group which provide the tools necessary for our analysis. The two key properties we consider are almost simplicity and the existence of a distortion element. Both will be defined and described in the lectures. Our techniques are almost all from low dimensional dynamics. But we are interested in how algebraic properties of a group -- commutativity, nilpotence, etc. affect the possible kinds of dynamics which can occur. For most of the results we will consider groups of diffeomorphisms which preserve a Borel probability measure. | |
| dc.identifier | https://arxiv.org/abs/0705.4054 | |
| dc.identifier | http://arxiv.org/abs/0705.4054 | |
| dc.identifier | Panoramas et Synth`eses, Soc. Math.de France {\bf 21} (2006) 35-52 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129570 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37E30;57S30 | |
| dc.title | Distortion in Groups of Circle and Surface Diffeomorphisms | |
| dc.type | text |