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Systems with Almost Specification Property May Have Zero Entropy

It is shown that there exist systems having almost specification property and zero entropy. Since Sigmund has shown that systems with specification property must have positive entropy, this result reveals further the difference between almost specification and specification. Moreover, one can step on to obtain a both sufficient and necessary condition to ensure positive entropy.

preprint2015arXivOpen access
Yiwei Dong
math.DSmath.SP
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Yiwei Dong

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