### A Criterion for a Process to Be Prime.

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

We extend the Davenport and Erdős construction of normal numbers to the ${\mathbb{Z}}^{d}$ case.

We prove a generalisation of the entropy formula for certain algebraic ${\mathbb{Z}}^{d}$-actions given in [2] and [4]. This formula expresses the entropy as the logarithm of the Mahler measure of a Laurent polynomial in d variables with integral coefficients. We replace the rational integers by the integers in a number field and examine the entropy of the corresponding dynamical system.

The purpose of this paper is to prove the existence of a free subgroup of the group of all affine transformations on the plane with determinant 1 such that the action of the subgroup is locally commutative.

A weighted ergodic maximal equality is proved for a conservative and ergodic semiflow of nonsingular automorphisms.

Analytic cocycles of type $II{I}_{0}$ over an irrational rotation are constructed and an example of that type is given, where all corresponding special flows are weakly mixing.