TY - JOUR
ID - 4050
TI - Entropy of infinite systems and transformations
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN -
AU - Amini, Massoud
AD - Department of Mathematics
Tarbiat Modares University
Tehran, Iran
Y1 - 2019
PY - 2019
VL - 10
IS - 1
SP - 27
EP - 33
KW - Infinite invariant measure
KW - Kolmogorov-Sinai entropy
KW - Parry entropy
KW - Krengel entropy
KW - Poisson entropy
KW - Pinsker factor
DO - 10.22075/ijnaa.2019.17400.1931
N2 - 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 infinite invariant measures. The three main extensions are Parry, Krengel, and Poisson entropies. In this survey, we shortly overview the history of entropy, discuss the pioneering notions of Shannon and later contributions of Kolmogorov and Sinai, and discuss in somewhat more details the extensions to infinite systems. We compare and contrast these entropies with each other and with the entropy on finite systems.
UR - https://ijnaa.semnan.ac.ir/article_4050.html
L1 - https://ijnaa.semnan.ac.ir/article_4050_8ffa4224508e953e9acfb96439027198.pdf
ER -