Ergodic measures for non-abelian compact group extensions
Ergodic Properties of Certain Surjective Cellular Automata.
Ergodic properties of generalized Lüroth series
Ergodic properties of group extensions of dynamical systems with discrete spectra
Ergodic group extensions of a dynamical system with discrete spectrum are considered. The elements of the centralizer of such a system are described. The main result says that each invariant sub-σ-algebra is determined by a compact subgroup in the centralizer of a normal natural factor.
Ergodic Properties of Invariant Measures for Piecewise Monotonic Transformations.
Ergodic properties of skew products with Lasota-Yorke type maps in the base
We consider skew products preserving a measure which is absolutely continuous with respect to the product measure. Here f is a 1-sided Markov shift with a finite set of states or a Lasota-Yorke type transformation and , i = 1,..., max e, are nonsingular transformations of some probability space. We obtain the description of the set of eigenfunctions of the Frobenius-Perron operator for T and consequently we get the conditions ensuring the ergodicity, weak mixing and exactness of T. We apply these...
Ergodic properties of skew products withfibre maps of Lasota-Yorke type
We consider the skew product transformation T(x,y)= (f(x), ) where f is an endomorphism of a Lebesgue space (X,A,p), e : X → S and is a family of Lasota-Yorke type maps of the unit interval into itself. We obtain conditions under which the ergodic properties of f imply the same properties for T. Consequently, we get the asymptotical stability of random perturbations of a single Lasota-Yorke type map. We apply this to some probabilistic model of the motion of cogged bits in the rotary drilling...
Ergodic properties of square-free numbers
We construct a natural invariant measure concentrated on the set of square-free numbers, and invariant under the shift. We prove that the corresponding dynamical system is isomorphic to a translation on a compact, Abelian group. This implies that this system is not weakly mixing and has zero measure-theoretical entropy.
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...