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 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 dominated ergodic estimate for spaces with weights
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 generalization of Steinhaus' theorem to coordinatewise measure preserving binary transformations
A generalization of the individual ergodic theorem
A generalized skew product
A Horseshoe with Positive Measure.
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 large set containing few orbits of measure preserving transformations.
A large set containing few orbits of measure preserving transformations. (Summary).
A limit theorem for the q-convolution
The q-convolution is a measure-preserving transformation which originates from non-commutative probability, but can also be treated as a one-parameter deformation of the classical convolution. We show that its commutative aspect is further certified by the fact that the q-convolution satisfies all of the conditions of the generalized convolution (in the sense of Urbanik). The last condition of Urbanik's definition, the law of large numbers, is the crucial part to be proved and the non-commutative...
A locally commutative free group acting on the plane
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.