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Observational Modeling of the Kolmogorov-Sinai Entropy

Journal: Sahand Communications in Mathematical Analysis (Vol.13, No. 1)

Publication Date:

Authors : ;

Page : 101-114

Keywords : Relative entropy; Relative semi-dynamical system; $m_\Theta$-equivalence; $m_\Theta$-generator; $ (\Theta_1; \Theta_2) $-isomorphism;

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In this paper, Kolmogorov-Sinai entropy is studied using mathematical modeling of an observer $ Theta $. The relative entropy of a sub-$ sigma_Theta $-algebra having finite atoms is defined and then   the ergodic properties of relative  semi-dynamical systems are investigated.  Also,  a relative version of Kolmogorov-Sinai theorem  is given. Finally, it is proved  that the relative entropy of a relative $ Theta $-measure preserving transformations with respect to a relative sub-$sigma_Theta$-algebra having finite atoms is affine.

Last modified: 2019-04-28 14:12:06