Ergodic Properties of the Erdös Measure, the Entropy of the Goldenshift, and Related Problems.
Ergodic theorem, reversibility and the filling scheme
The aim of this short note is to present in terse style the meaning and consequences of the "filling scheme" approach for a probability measure preserving transformation. A cohomological equation encapsulates the argument. We complete and simplify Woś' study (1986) of the reversibility of the ergodic limits when integrability is not assumed. We give short and unified proofs of well known results about the behaviour of ergodic averages, like Kesten's lemma (1975). The strikingly simple proof of the...
Ergodic theorems for linear operators on with strict topology
Ergodic Theorems for Noncommutative Dynamical Systems.
Ergodic theorems for subadditive superstationary families of random sets with values in Banach spaces
Under different compactness assumptions pointwise and mean ergodic theorems for subadditive superstationary families of random sets whose values are weakly (or strongly) compact convex subsets of a separable Banach space are presented. The results generalize those of [14], where random sets in are considered. Techniques used here are inspired by [3].
Ergodic theory and connections with analysis and probability.
Ergodic theory, entropy, and coding problems of information theory
Ergodic Theory for Complex Continued Fractions.
Ergodic theory for inner functions of the upper half plane
Ergodic theory for the one-dimensional Jacobi operator
We determine the number and properties of the invariant measures under the projective flow defined by a family of one-dimensional Jacobi operators. We calculate the derivative of the Floquet coefficient on the absolutely continuous spectrum and deduce the existence of the non-tangential limit of Weyl m-functions in the -topology.
Ergodic theory, semisimple Lie groups and foliations by manifolds of negative curvature
Ergodic transforms associated to general averages
Jones and Rosenblatt started the study of an ergodic transform which is analogous to the martingale transform. In this paper we present a unified treatment of the ergodic transforms associated to positive groups induced by nonsingular flows and to general means which include the usual averages, Cesàro-α averages and Abel means. We prove the boundedness in , 1 < p < ∞, of the maximal ergodic transforms assuming that the semigroup is Cesàro bounded in . For p = 1 we find that the maximal ergodic...
Ergodic -extensions over rational pure point spectrum, category and homomorphisms
Ergodicité d'une transformation cylindrique
Ergodicité et pureté des produits de Riesz
On montre que les produits de Riesz sur le tore sont des mesures ergodiques sous une condition de lacunarité pour les fréquences, indépendamment de toute propriété arithmétique, et que cette condition est la meilleure possible de ce point de vue. On établit un critère analogue pour la propriété de pureté discutés précédemment par B. Host et l’auteur, ce qui fournit l’exemple d’une mesure pure étrangère à toutes ses translatées et en particulier non ergodique.
Ergodicité intrinsèque de produits fibrés d'applications chaotiques unidimensionnelles
Ergodicity and asymptotically almost periodic solutions of some differential equations.
Ergodicity and extremality of AMS sources and channels.
Ergodicity and Weak-Mixing of Homogeneous Extensions of Measure-Preserving Transformations with Applications to Markov Shifts.
Ergodicity for piecewise smooth cocycles over toral rotations
Let α be an ergodic rotation of the d-torus . For any piecewise smooth function with sufficiently regular pieces the unitary operator Vh(x) = exp(2π if(x))h(x + α) acting on is shown to have a continuous non-Dirichlet spectrum if the gradient of f has nonzero integral. In particular, the resulting skew product must be ergodic. If in addition α is sufficiently well approximated by rational vectors and f is represented by a linear function with noninteger coefficients then the spectrum of V...