### A chaotic function with zero topological entropy having a non-perfect attractor

### A class of generalized Ornstein transformations with the weak mixing property

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

### A criterion for Toeplitz flows to be topologically isomorphic and applications

A dynamical system is said to be coalescent if its only endomorphisms are automorphisms. The question whether there exist coalescent ergodic dynamical systems with positive entropy has not been solved so far and it seems to be difficult. The analogous problem in topological dynamics has been solved by Walters ([W]). His example, however, is not minimal. In [B-K2], a class of strictly ergodic (hence minimal) Toeplitz flows is presented, which have positive entropy and trivial topological centralizers...

### A cut salad of cocycles

We study the centraliser of locally compact group extensions of ergodic probability preserving transformations. New methods establishing ergodicity of group extensions are introduced, and new examples of squashable and non-coalescent group extensions are constructed.

### A cylinder flow arising from irregularity of distribution

### A ${\mathbb{Z}}^{d}$ generalization of the Davenport-Erdős construction of normal numbers

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

### A Decomposition Theorem for Additive Set-Functions, with Applications to Pettis Integrals and Ergodic Means.

### A description of stochastic systems using chaotic maps.

### A Differentiation Theorem for Additive Processes.

### A dimension group for local homeomorphisms and endomorphisms of onesided shifts fo finite type.

### A dominated ergodic estimate for ${L}_{p}$ spaces with weights

### A dynamical interpretation of the global canonical height on an elliptic curve.

### A Ford-Fulkerson type theorem concerning vector-valued flows in infinite networks

### A Formula for Popp’s Volume in Sub-Riemannian Geometry

For an equiregular sub-Riemannian manifold M, Popp’s volume is a smooth volume which is canonically associated with the sub-Riemannian structure, and it is a natural generalization of the Riemannian one. In this paper we prove a general formula for Popp’s volume, written in terms of a frame adapted to the sub-Riemannian distribution. As a first application of this result, we prove an explicit formula for the canonical sub- Laplacian, namely the one associated with Popp’s volume. Finally, we discuss...

### A Function with Countably Many Ergodic Equilibrium States.

### A generalisation of Mahler measure and its application in algebraic dynamical systems

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.

### A generalization of Steinhaus' theorem to coordinatewise measure preserving binary transformations

### A generalization of the individual ergodic theorem