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...
Ergodicity of a class of cylinder flows related to irregularities of distribution
Ergodické prelúdium
Ergodische Eigenschaften affiner Modulo-1-Transformationen.
Erratum to: On the Infinite Product Construction of Non-Singular Transformations of a Measure Space.
Estimations de la dimension inférieure et de la dimension supérieure des mesures
Etude spectrale des substitutions de longueur constante
Exactness of expanding mappings
Existence of discrete ergodic singular transforms for admissible processes
This article is concerned with the study of the discrete version of generalized ergodic Calderón-Zygmund singular operators. It is shown that such discrete ergodic singular operators for a class of superadditive processes, namely, bounded symmetric admissible processes relative to measure preserving transformations, are weak (1,1). From this maximal inequality, a.e. existence of the discrete ergodic singular transform is obtained for such superadditive processes. This generalizes the well-known...
Existence of invariant measures for piecewise continuous transformations
Existence of time averages from the topological point of view
Explicit construction of normal lattice configurations
We extend Champernowne’s construction of normal numbers to base b to the case and obtain an explicit construction of a generic point of the shift transformation of the set .
Extending quasi-invariant measures by using subgroups of a given group.
Extension of the Birkhoff and von Neumann ergodic theorems to semigroup actions
Extensions de systèmes dynamiques par des endomorphismes de groupes compacts
Extensions of Cocycles for Hyperfinite Actions and Applications.