Uniform endomorphisms which are isomorphic to a Bernoulli shift

dc.creatorHoffman, Christopher
dc.creatorRudolph, Daniel
dc.date2004-11-22
dc.date.accessioned2026-07-07T05:14:35Z
dc.date.available2026-07-07T05:14:35Z
dc.descriptionA {\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.description23 pages, published version
dc.identifierhttps://arxiv.org/abs/math/0411494
dc.identifierhttp://arxiv.org/abs/math/0411494
dc.identifierAnn. of Math. (2), Vol. 156 (2002), no. 1, 79--101
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73330
dc.subjectDynamical Systems
dc.subject37A35 (Primary) 28D05, 37A05, 37B10 (Secondary)
dc.titleUniform endomorphisms which are isomorphic to a Bernoulli shift
dc.typetext

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