Geodesic
Scaling entropy of unstable systems
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXI, Tome 498 (2020), pp. 5-17

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In this paper, we study the slow entropy-type invariant of a dynamic system proposed by A. M. Vershik. We provide an explicit construction of a system that has an empty class of scaling entropy sequences. For this unstable case, we introduce an upgraded notion of the invariant, generalize the subadditivity results, and provide an exhaustive series of examples. 
@article{ZNSL_2020_498_a0,
     author = {G. A. Veprev},
     title = {Scaling entropy of unstable systems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--17},
     publisher = {mathdoc},
     volume = {498},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_498_a0/}
}
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G. A. Veprev. Scaling entropy of unstable systems. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXI, Tome 498 (2020), pp. 5-17. http://geodesic.mathdoc.fr/item/ZNSL_2020_498_a0/