The Pascal Adic Transformation is Loosely Bernoulli

The Pascal Adic Transformation is Loosely Bernoulli Elise Janvresse, Thierry de la Rue CNRS - UMR 6085 Abstract The Pascal adic transformation is one of the simplest examples of adic transformations. We recall its construction by cutting and stacking and prove that it is loosely Bernoulli. Key-words : adic transformation, loosely Bernoulli systems. Classification AMS 2000: 28D05 La transformation Pascal adique est lachement Bernoulli. Resume La transformation Pascal adique est un des exemples les plus simples de transformations adiques. Nous rappelons sa construction par decoupage et empilement et montrons qu'elle est lachement Bernoulli. Mots-clefs : transformation adique, systemes lachement Bernoulli. 1 Introduction The notion of adic transformation has been introduced by Vershik (see e.g. [5], [4]), as a model in which the transformation acts on infinite paths in some graphs, called Bratteli diagrams. As shown by Vershik, every ergodic automor- phism of the Lebesgue space is isomorphic to some adic transformation, with a Bratteli diagram which may be quite complicated. Vershik also proposed to study the ergodic properties of an adic transformation in a given simple graph, such as the Pascal graph which gives rise to the so-called Pascal adic transformation. 1.1 The Pascal adic transformation Here we recall the construction and some basic properties of the Pascal adic transformation with parameter p, following the cutting and stacking model exposed in [2].

• lebesgue measure


• called pascal adic


• has zero


• entropy measure preserving


• pascal adic


• transformation