Open Access
Research Article
Rotational Entropy of an Annular Iterated Functions System
*Fatemeh RezaeiCorresponding authorf_rezaaei@yahoo.comDepartment of MathematicsYazd UniversityIranView full profile → , Mehdi Fatehi Niafatehiniam@yazd.ac.irDepartment of MathematicsYazd UniversityIranView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 05 Nov 2020
- Accepted:
- 17 Aug 2021
- Published Online:
- 04 Jan 2022
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- 1726037X.2021.2009199
- Pages:
- 189–202
Abstract
In this article, we consider an iterated functions system (IFS) whose functions are homeomorphisms on an annulus. We define rotational spanning and separating sets for the IFS and then provide two definitions for the rotational entropy of the IFS. We show that in the IFSs, the rotational entropy is a topological invariant. We prove that the rotational entropy of an annular IFS is equal to the rotational entropy on its non-wandering set for sequences of functions with a specific condition.
Keywords
Subject Classifications
54H2037B55
References
- Roy L.Adler, Alan G.Knoheim, and, M.Harry McAndrew, Topological entropy , Transactions of the American Mathematical Society , Vol. 114 , Number 2, 309-319 (1965).
- FernandaBotelho, Rotational entropy for annulus endomorphisms , Pacific journal of mathematics , Vol. 151 , Number 1 , 1 - 19 ( 1991 ). doi: 10.2140/pjm.1991.151.1
- RufusBowen, Topological entropy and axiom A, In Proc. Sympos . Pure Math , Vol. 14 , 23 - 41 ( 1970 ).
- Rudolf Clausius, Über die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärmelehre selbst ableiten lassen , Journal of Annalen der Physik , Vol. 155 , Number 3 , 368 - 397 ( 1850 ). doi: 10.1002/andp.18501550306
- TomaszDownarowicz, Entropy in dynamical systems , Vol. 18 , Cambridge University Press , 2011 .
- ToddFisher, Lecture 10, Computing Topological Entropy, Brigham Young University, https://math.byu.edu/tfisher/documents/classes/2008/winter/635/Lecture10.pdf , 2008.
- Mehdi FatehiNia, Iterated function systems with the shadowing property , Advanced research in pure mathematics , Vol. 7 , Number 1 , 83 - 91 ( 2015 ), doi: 10.5373/jarpm.2079.070214 .
- Andrei NikolaevitchKolmogorov, Entropy per unit time as a metric invariant of automorphisms , Dokl. Akad. Nauk SSSR , Vol. 124 , Number 4 , 754 - 755 ( 1959 ).
- SergiiKolyada, and LubomirSnoha, Topological entropy of nonautonomous dynamical systems , Random and computational dynamics , Vol. 4 , Number 2 , 205 ( 1996 ).
- Yakov GrigorevichSinai, On the concept of entropy for a dynamic system , Dokl. Akad. Nauk SSSR , Vol. 124 , Number 4 , 768 - 771 ( 1959 ).
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