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A class of nonmixing dynamical systems with monotonic semigroup property

โœ Scribed by M. Courbage; D. Hamdan


Publisher
Springer
Year
1991
Tongue
English
Weight
248 KB
Volume
22
Category
Article
ISSN
0377-9017

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โœฆ 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.


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