TY - JOUR

T1 - Kolmogorov-sinai entropy via separation properties of order-generated σ-Algebras

AU - Antoniouk, Alexandra

AU - Keller, Karsten

AU - Maksymenko, Sergiy

PY - 2014/5/1

Y1 - 2014/5/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84886576886&partnerID=8YFLogxK

U2 - 10.3934/dcds.2014.34.1793

DO - 10.3934/dcds.2014.34.1793

M3 - Journal articles

AN - SCOPUS:84886576886

SN - 1078-0947

VL - 34

SP - 1793

EP - 1809

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 5

ER -