Dynamical properties of the Pascal adic transformation.

            Xavier Mela and Karl Petersen


  This interesting transformation defined as an adic by A. Vershik can
also be represented by cutting and stacking or as a subshift on a finite
alphabet determined by a countable family of substitutions. Its ergodic
invariant measures have been identified (this is basically equivalent to
the theorems of Hewitt-Savage and de Finetti), and, while weak mixing for
these measures remains open, progress is being made on other dynamical
properties, such as topological weak mixing, complexity, asymptotics of
return times to cylinders, the loose Bernoulli property (by de la Rue and
Janvresse), and local rank 1.