The Ergodic Theory of Axiom A Flows.
The ergodic theory of positive operators on continuous functions
The filling scheme and the ergodic theorems of Kesten and Tanny
The generalized Boole's transofrmation is ergodic.
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 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 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 Prime Orbit Theorem for Quasihyperbolic Toral Automorphisms.
The problem of -simple spectrum for ergodic group automorphisms
The rate of convergence of iterates of the Frobenius-Perron operator for piecewise monotonic transformations
The rearrangement inequality for the ergodic maximal function.
The return time theorem fails on infinite measure-preserving systems