Uniform endomorphisms which are isomorphic to a Bernoulli shift
| dc.creator | Hoffman, Christopher | |
| dc.creator | Rudolph, Daniel | |
| dc.date | 2004-11-22 | |
| dc.date.accessioned | 2026-07-07T05:14:35Z | |
| dc.date.available | 2026-07-07T05:14:35Z | |
| dc.description | A {\it uniformly $p$-to-one endomorphism} is a measure-preserving map with entropy log $p$ which is almost everywhere $p$-to-one and for which the conditional expectation of each preimage is precisely $1/p$. The {\it standard} example of this is a one-sided $p$-shift with uniform i.i.d. Bernoulli measure. We give a characterization of those uniformly finite-to-one endomorphisms conjugate to this standard example by a condition on the past tree of names which is analogous to {\it very weakly Bernoulli} or {\it loosely Bernoulli.} As a consequence we show that a large class of isometric extensions of the standard example are conjugate to it. | |
| dc.description | 23 pages, published version | |
| dc.identifier | https://arxiv.org/abs/math/0411494 | |
| dc.identifier | http://arxiv.org/abs/math/0411494 | |
| dc.identifier | Ann. of Math. (2), Vol. 156 (2002), no. 1, 79--101 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73330 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37A35 (Primary) 28D05, 37A05, 37B10 (Secondary) | |
| dc.title | Uniform endomorphisms which are isomorphic to a Bernoulli shift | |
| dc.type | text |