On Dimensional Functions and Topological Markov Chains.
On disjointness properties of some smooth flows
Special flows over some locally rigid automorphisms and under L² ceiling functions satisfying a local L² Denjoy-Koksma type inequality are considered. Such flows are proved to be disjoint (in the sense of Furstenberg) from mixing flows and (under some stronger assumption) from weakly mixing flows for which the weak closure of the set of all instances consists of indecomposable Markov operators. As applications we prove that ∙ special flows built over ergodic interval exchange...
On Ergodic Averages for Affine Lattice Actions on Tori.
On Ergodic Flows and the Isomorphism of Factors.
On Ergodic Properties of Inner Functions.
On ergodic singular integral operators
On Ergodic Theory of A. Schmidt's Complex Continued Fractions over Gaussian Field.
On Exact Toral Endomorphisms.
On extremal and perfect σ-algebras for -actions on a Lebesgue space
We show that for every positive integer d there exists a -action and an extremal σ-algebra of it which is not perfect.
On extremal and perfect σ-algebras for flows
It is shown that there exists a flow on a Lebesgue space with finite entropy and an extremal σ-algebra of it which is not perfect.
On Fréchet theorem in the set of measure preserving functions over the unit interval.
On functions with bounded remainder
Let be a von Neumann-Kakutani - adic adding machine transformation and let . PutWe study three questions:1. When will be bounded?2. What can be said about limit points of 3. When will the skew product be ergodic on
On Generators for Ergodic Flowers.
On group extensions of 2-fold simple ergodic actions
Compact group extensions of 2-fold simple actions of locally compact second countable amenable groups are considered. It is shown what the elements of the centralizer of such a system look like. It is also proved that each factor of such a system is determined by a compact subgroup in the centralizer of a normal factor.
On invariant elements for positive operators.
In the paper we study the existence of nonzero positive invariant elements for positive operators in Riesz spaces. The class of Riesz spaces for which the results are valid is large enough to contain all the Banach lattices with order continuous norms. All the results obtained in earlier works deal with positive operators in KB-spaces and in many of them the approach is based upon the use of Banach limits. The methods created for KB-spaces cannot be extended to our more general setting; that is...
On invariant functions for positive operators
On invariant measures for piecewise -transformations of the n-dimensional cube
On invariant measures for piecewise convex transformations
On invariant measures for some infinite-dimensional dynamical systems
On invariant measures for the tend map.
The bifurcation structure of a one parameter dependent piecewise linear population model is described. An explicit formula is given for the density of the unique invariant absolutely continuous probability measure mub for each parameter value b. The continuity of the map b --> mub is established.