A class of nonmixing dynamical systems with monotonic semigroup property

✍ Scribed by M. Courbage; D. Hamdan

• Publisher: Springer
• Year: 1991
• Tongue: English
• Weight: 248 KB
• Volume: 22
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00405173

✦ Synopsis

In order to illustrate the class of conservative dynamical systems for which a Boltzmann entropy can be obtained under finite coarse-graining [2], we consider dynamical systems defined by the shift transformation on K e, where K is any finite set of integers. We give a class of non-Markovian invanant measures that verify the Chapman-Kolmogorov equation (equivalent to a Boltzmann entropy) for any positive stochastic matrix and that are ergodic but not weakly mixing.