On infinite Nielsen transformations.

Entropy of infinite systems and transformations

The Kolmogorov-Sinai entropy is a far reaching dynamical generalization of Shannon entropy of information systems. This entropy works perfectly for probability measure preserving (p.m.p.) transformations. However, it is not useful when there is no finite invariant measure. There are certain successful extensions of the notion of entropy to infinite measure spaces, or transformations with ...

Transformations of logic programs on infinite lists

We consider an extension of logic programs, called ω-programs, that can be used to define predicates over infinite lists. ω-programs allow us to specify properties of the infinite behavior of reactive systems and, in general, properties of infinite sequences of events. The semantics of ω-programs is an extension of the perfect model semantics. We present variants of the familiar unfold/fold rul...

Transformations of measure on infinite-dimensional vector spaces∗

On Young towers associated with infinite measure preserving transformations

For a σ-finite measure preserving dynamical system (X,μ, T ), we formulate necessary and sufficient conditions for a Young tower (∆, ν, F ) to be a (measure theoretic) extension of the original system. Because F is pointwise dual ergodic by construction, one immediate consequence of these conditions is that the Darling Kac theorem carries over from F to T . One advantage of the Darling Kac theo...

Infinite Measure Preserving Transformations with "mixing"