Rigidity of joinings for some measure-preserving systems

Some Observations on Dirac Measure-Preserving Transformations and their Results

Dirac measure is an important measure in many related branches to mathematics. The current paper characterizes measure-preserving transformations between two Dirac measure spaces or a Dirac measure space and a probability measure space. Also, it studies isomorphic Dirac measure spaces, equivalence Dirac measure algebras, and conjugate of Dirac measure spaces. The equivalence classes of a Dirac ...

Measure Preserving Systems

Weak disjointness of measure preserving dynamical systems

Two measure preserving dynamical systems are weakly disjoint if some pointwise convergence property is satisfied by ergodic averages on their direct product (a precise definition is given below). Disjointness implies weak disjointness. We start studying this new concept, both by stating some general properties and by giving various examples. The content of the article is summarized in the intro...

Rigidity of harmonic measure

Let J be the Julia set of a conformal dynamics f . Provided that f is polynomial-like we prove that the harmonic measure on J is mutually absolutely continuous with the measure of maximal entropy if and only if f is conformally equivalent to a polynomial. This is no longer true for generalized polynomial-like maps. But for such dynamics the coincidence of classes of these two measures turns out...

Measure-preserving Dynamical Systems and Approximation Techniques

In this paper, we demonstrate how approximation structures called sufficient semirings can provide information about measure-preserving dynamical systems. We describe the basic properties of measure-preserving dynamical systems and illustrate their connections to sufficient semirings by investigating the dyadic adding machine.