Result: Sufficient families and entropy of inverse limit

Title:
Sufficient families and entropy of inverse limit
Authors:
Khare, Mona
Publisher Information:
Slovak Academy of Sciences, Mathematical Institute, Bratislava; De Gruyter, Warsaw
Subject Terms:
Dynamical systems and their relations with probability theory and stochastic processes, generator, atom, inverse spectrum of \(F\)-dynamical systems, Entropy and other invariants, isomorphism, classification in ergodic theory, \(F\)-probability measure space, entropy, \(F\)-dynamical system
Document Type:
Academic journal Article
File Description:
application/xml
Access URL:
https://zbmath.org/1510638
Accession Number:
edsair.c2b0b933574d..fd67c5a321426ffc42b91d242b4aa27c
Database:
OpenAIRE

Further Information

Summary: The purpose of the present paper is to study the metric entropy \(h(\phi , \mathcal N)\) of an \(F\)-measure preserving transformation \(\phi \) relative to a \(\sigma \)-algebra \(\mathcal N\) of an \(F\)-dynamical system. Concepts of sufficient families and generators are introduced and a few results are proved. Finally, the entropy of the inverse limit of an inverse spectrum of \(F\)-dynamical systems is obtained.