Non-ergodicity for C^1 Expanding Maps
| dc.creator | Quas, Anthony N. | |
| dc.date | 1993-03-31 | |
| dc.date.accessioned | 2026-07-07T09:07:36Z | |
| dc.date.available | 2026-07-07T09:07:36Z | |
| dc.description | In this paper, we consider the question of existence and uniqueness of absolutely continuous invariant measures for expanding $C^1$ maps of the circle. This is a question which arises naturally from results which are known in the case of expanding $C^k$ maps of the circle where $k\geq 2$, or even $C^{1+ε}$ expanding maps of the circle. In these cases, it is known that there exists a unique absolutely continuous invariant probability measure by the so-called `Folklore Theorem'. It follows that this measure is ergodic. It has been shown however that for $C^1$ maps there need not be any such measure. However, this leaves the question of whether there can be more than one such measure for $C^1$ expanding maps of the circle. This is the subject of this paper, and in it, we show that there exists a $C^1$ expanding map of the circle which has more than one absolutely continuous invariant probability measure. | |
| dc.description | 7 pages, uses MSSYMB (non-essential) | |
| dc.identifier | https://arxiv.org/abs/chao-dyn/9303018 | |
| dc.identifier | http://arxiv.org/abs/chao-dyn/9303018 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150424 | |
| dc.subject | Chaotic Dynamics | |
| dc.title | Non-ergodicity for C^1 Expanding Maps | |
| dc.type | text |