Abstract
We show that a solenoid is a dynamical object and we express its complexity by a number of different entropy-like quantities in Hurley's sense. Some relations between these entropy-like quantities are presented. We adopt the theory of Carathéodory dimension structures introduced axiomatically by Pesin to a case of a solenoid. Any of the above mentioned entropy-like quantities determines a particular Carathéodory structure such that its upper capacity coincides with the considered quantity. We mimic a definition of the local measure entropy, introduced by Brin and Katok for a single map, to a case of a solenoid. Lower estimations of these quantities by corresponding local measure entropies are described.
Citation
Andrzej Biś. Wojciech Kozłowski. "Some Remarks on Dynamical System of Solenoids." Taiwanese J. Math. 22 (6) 1463 - 1478, December, 2018. https://doi.org/10.11650/tjm/180506
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