## On the entropy of dynamical systems in product MV algebras.(English)Zbl 0983.37007

From the introduction: The notion of the entropy of a dynamical system has been defined and studied for distinguishing non-isomorphic dynamical systems. If two dynamical systems are isomorphic, they have the same entropy. Therefore, systems with different entropies cannot be isomorphic. If one substitutes in the definition of entropy, the notion of a set partition by the notion of fuzzy partition, a larger class of invariants can be obtained.
We generalize these results considering the general notion of the product MV algebra and obtain some standard assertions, the Kolmogorov theorem on generators being omitted. Namely, in the general situation we have no satisfactory version of the martingale convergence theorem.

### MSC:

 37A35 Entropy and other invariants, isomorphism, classification in ergodic theory 06D35 MV-algebras

### Keywords:

entropy; fuzzy partition; product MV algebra
Full Text:

### References:

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