Polynomial Entropy of Subsets for Free Semigroup Actions

Polynomial Entropy of Subsets for Free Semigroup Actions

In this paper, we introduce the notions of polynomial entropy on an arbitrary subset and lower local polynomial entropy for free semigroup actions. Also, we give some properties of Bowen polynomial entropy and discuss the relation between Bowen topological entropy and Bowen polynomial entropy in the...

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Veröffentlicht in:Journal of dynamical and control systems 2023, Vol.29 (1), p.229-243
Hauptverfasser: Liu, Lei, Zhao, Cao
Format: Artikel
Sprache:eng
Schlagworte:
Calculus of Variations and Optimal Control
Optimization
Control
Dynamical Systems
Dynamical Systems and Ergodic Theory
Entropy
Mathematics
Mathematics and Statistics
Polynomials
Semigroups
Systems Theory
Vibration
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Zusammenfassung:In this paper, we introduce the notions of polynomial entropy on an arbitrary subset and lower local polynomial entropy for free semigroup actions. Also, we give some properties of Bowen polynomial entropy and discuss the relation between Bowen topological entropy and Bowen polynomial entropy in the context of free semigroup actions. Finally, we investigate the relation between lower local polynomial entropy of Borel probability measures and Bowen polynomial entropy for free semigroup actions.
ISSN:1079-2724
1573-8698
DOI:10.1007/s10883-021-09572-z