Kolmogorov-sinai entropy via separation properties of order-generated σ-Algebras

Alexandra Antoniouk, Karsten Keller, Sergiy Maksymenko

9 Citations (Scopus)


In a recent paper, K. Keller has given a characterization of the Kolmogorov-Sinai entropy of a discrete-time measure-preserving dynamical system on the base of an increasing sequence of special partitions. These partitions are constructed from order relations obtained via a given real-valued random vector, which can be interpreted as a collection of observables on the system and is assumed to separate points of it. In the present paper we relax the separation condition in order to generalize the given characterization of Kolmogorov-Sinai entropy, providing a statement on equivalence of σ-algebras. On its base we show that in the case that a dynamical system is living on an m-dimensional smooth manifold and the underlying measure is Lebesgue absolute continuous, the set of smooth random vectors of dimension n > m with given characterization of Kolmogorov-Sinai entropy is large in a certain sense.

Original languageEnglish
JournalDiscrete and Continuous Dynamical Systems- Series A
Issue number5
Pages (from-to)1793-1809
Number of pages17
Publication statusPublished - 01.05.2014


Dive into the research topics of 'Kolmogorov-sinai entropy via separation properties of order-generated σ-Algebras'. Together they form a unique fingerprint.

Cite this