### A characterization of partition polynomials and good Bernoulli trial measures in many symbols

Consider an experiment with d+1 possible outcomes, d of which occur with probabilities $x\u2081,...,{x}_{d}$. If we consider a large number of independent occurrences of this experiment, the probability of any event in the resulting space is a polynomial in $x\u2081,...,{x}_{d}$. We characterize those polynomials which arise as the probability of such an event. We use this to characterize those x⃗ for which the measure resulting from an infinite sequence of such trials is good in the sense of Akin.

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

### A class of nonstationary adic transformations

### A criterion of asymptotic stability for Markov-Feller e-chains on Polish spaces

Stettner [Bull. Polish Acad. Sci. Math. 42 (1994)] considered the asymptotic stability of Markov-Feller chains, provided the sequence of transition probabilities of the chain converges to an invariant probability measure in the weak sense and converges uniformly with respect to the initial state variable on compact sets. We extend those results to the setting of Polish spaces and relax the original assumptions. Finally, we present a class of Markov-Feller chains with a linear state space model which...

### 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 description of stochastic systems using chaotic maps.

### A descriptive view of unitary group representations

In this paper, we will study the relative complexity of the unitary duals of countable groups. In particular, we will explain that if $G$ and $H$ are countable amenable non-type I groups, then the unitary duals of $G$ and $H$ are Borel isomorphic.

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

### A distributionally chaotic triangular map with zero sequence topological entropy.

### A dual approach to triangle sequences: a multidimensional continued fraction algorithm.

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

### A family of stationary processes with infinite memory having the same p-marginals. Ergodic and spectral properties

We construct a large family of ergodic non-Markovian processes with infinite memory having the same p-dimensional marginal laws of an arbitrary ergodic Markov chain or projection of Markov chains. Some of their spectral and mixing properties are given. We show that the Chapman-Kolmogorov equation for the ergodic transition matrix is generically satisfied by infinite memory processes.

### A fibered system associated with the prime number sequence. (Sur un système fibré lié à la suite des nombres premiers.)

### A Gauss-Kuzmin theorem for the Rosen fractions

Using the natural extensions for the Rosen maps, we give an infinite-order-chain representation of the sequence of the incomplete quotients of the Rosen fractions. Together with the ergodic behaviour of a certain homogeneous random system with complete connections, this allows us to solve a variant of Gauss-Kuzmin problem for the above fraction expansion.

### A Gauss-Kuzmin-Lévy theorem for a certain continued fraction.

### A generalization of Straube's theorem: existence of absolutely continuous invariant measures for random maps.

### A joint limit theorem for compactly regenerative ergodic transformations

We study conservative ergodic infinite measure preserving transformations satisfying a compact regeneration property introduced by the second-named author in J. Anal. Math. 103 (2007). Assuming regular variation of the wandering rate, we clarify the asymptotic distributional behaviour of the random vector (Zₙ,Sₙ), where Zₙ and Sₙ are respectively the time of the last visit before time n to, and the occupation time of, a suitable set Y of finite measure.

### A map maintaining the orbits of a given ${\mathbb{Z}}^{d}$-action

Giordano et al. (2010) showed that every minimal free ${\mathbb{Z}}^{d}$-action of a Cantor space X is orbit equivalent to some ℤ-action. Trying to avoid the K-theory used there and modifying Forrest’s (2000) construction of a Bratteli diagram, we show how to define a (one-dimensional) continuous and injective map F on X∖one point such that for a residual subset of X the orbits of F are the same as the orbits of a given minimal free ${\mathbb{Z}}^{d}$-action.

### A matrix formalism for conjugacies of higher-dimensional shifts of finite type

We develop a natural matrix formalism for state splittings and amalgamations of higher-dimensional subshifts of finite type which extends the common notion of strong shift equivalence of ℤ⁺-matrices. Using the decomposition theorem every topological conjugacy between two ${\mathbb{Z}}^{d}$-shifts of finite type can thus be factorized into a finite chain of matrix transformations acting on the transition matrices of the two subshifts. Our results may be used algorithmically in computer explorations on topological...