The fractal dimension of invariant subsets for piecewise monotonic maps on the interval.
The generalized Boole's transofrmation is ergodic.
The generalized purity law for ergodic measures: a simple proof
The generic transformation has roots of all orders
In the sense of the Baire Category Theorem we show that the generic transformation T has roots of all orders (RAO theorem). The argument appears novel in that it proceeds by establishing that the set of such T is not meager - and then appeals to a Zero-One Law (Lemma 2). On the group Ω of (invertible measure-preserving) transformations, §D shows that the squaring map p: S → S^{2} is topologically complex in that both the locally-dense and locally-lacunary points of p are dense (Theorem 23). The...
The Geometry of Model Spaces for Probability-Preserving Actions of Sofic Groups
Bowen’s notion of sofic entropy is a powerful invariant for classifying probability-preserving actions of sofic groups. It can be defined in terms of the covering numbers of certain metric spaces associated to such an action, the ‘model spaces’. The metric geometry of these model spaces can exhibit various interesting features, some of which provide other invariants of the action. This paper explores an approximate connectedness property of the model spaces, and uses it give a new proof that certain...
The Group of Measure-Preserving Transformations of [0,1) has no Outer Automorphisms.
The Horocycle Flow is Mixing of all Degrees.
The integral analog of a series with a two-point sum range.
The Kantorovich metric: the initial history and little-known applications.
The law of exponential decay for expanding mappings
The law of exponential decay for r-adic transformations
The Markov process determined by a weighted composition operator
The metrical theory of complex continued fractions
The Morse minimal system is finitarily Kakutani equivalent to the binary odometer
Two invertible dynamical systems (X,,μ,T) and (Y,,ν,S), where X and Y are Polish spaces and Borel probability spaces and T, S are measure preserving homeomorphisms of X and Y, are said to be finitarily orbit equivalent if there exists an invertible measure preserving mapping ϕ from a subset X₀ of X of measure one onto a subset Y₀ of Y of full measure such that (1) is continuous in the relative topology on X₀ and is continuous in the relative topology on Y₀, (2) for μ-a.e. x ∈ X. (X,,μ,T) and...
The Motion of Disks in a Torus
The multiplier-series of a Schottky group.
The one-sided ergodic Hilbert transform in Banach spaces
Let T be a power-bounded operator on a (real or complex) Banach space. We study the convergence of the one-sided ergodic Hilbert transform . We prove that weak and strong convergence are equivalent, and in a reflexive space also is equivalent to the convergence. We also show that (which converges on (I-T)X) is precisely the infinitesimal generator of the semigroup .
The Pascal adic transformation is loosely Bernoulli
The Poisson formula for groups with hyperbolic properties.
The Prime Orbit Theorem for Quasihyperbolic Toral Automorphisms.