Open Access
December, 2018 Some Remarks on Dynamical System of Solenoids
Andrzej Biś, Wojciech Kozłowski
Taiwanese J. Math. 22(6): 1463-1478 (December, 2018). DOI: 10.11650/tjm/180506


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.


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Andrzej Biś. Wojciech Kozłowski. "Some Remarks on Dynamical System of Solenoids." Taiwanese J. Math. 22 (6) 1463 - 1478, December, 2018.


Received: 3 August 2017; Revised: 4 May 2018; Accepted: 20 May 2018; Published: December, 2018
First available in Project Euclid: 9 June 2018

zbMATH: 1405.37022
MathSciNet: MR3880237
Digital Object Identifier: 10.11650/tjm/180506

Primary: 28D20 , 37B45
Secondary: 54F45 , 54H20‎

Keywords: Carathéodory structure , Entropy , entropy-like quantity , local measure entropy , solenoids

Rights: Copyright © 2018 The Mathematical Society of the Republic of China

Vol.22 • No. 6 • December, 2018
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