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http://dx.doi.org/10.5831/HMJ.2020.42.4.681

TOPOLOGICAL ENTROPY OF ONE DIMENSIONAL ITERATED FUNCTION SYSTEMS  

Nia, Mehdi Fatehi (Department of Mathematics,Yazd University)
Moeinaddini, Fatemeh (Department of Mathematics,Yazd University)
Publication Information
Honam Mathematical Journal / v.42, no.4, 2020 , pp. 681-699 More about this Journal
Abstract
In this paper, topological entropy of iterated function systems (IFS) on one dimensional spaces is considered. Estimation of an upper bound of topological entropy of piecewise monotone IFS is obtained by open covers. Then, we provide a way to calculate topological entropy of piecewise monotone IFS. In the following, some examples are given to illustrate our theoretical results. Finally, we have a discussion about the possible applications of these examples in various sciences.
Keywords
Entropy; Iterated Function System; Logistic function; Piecewise monotone; Tent map;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 R. Adler, A. Konheim and M. McAndrew, Topological entropy, Trans. Amer. Math. Soc, 114 (1965), 309-319.   DOI
2 AlsedA, LluAs, J. Llibre, and M. Misiurewicz, Combinatorial dynamics and entropy in dimension one, World Scientific Publishing Company (2000).
3 L. Alsed'a, S. Kolyada, J. Llibre and L. Snoha, Axiomatic Definition of the Topological Entropy on the Interval, Aequationes Math 65, 1-2 (2003), 113-132.   DOI
4 M.F. Barnsley and A. Vince, The Conley attractor of an iterated function system, Bull. Aust. Math. Soc, 88 (2013), 267-279.   DOI
5 J. Baez, classical Mechanics, Lecture, 14 (February 26, 2008).
6 Berryman and A. Alan, The orgins and evolution of predator-prey theory, Ecology, 73.5 (1992), 1530-1535.   DOI
7 R. Bowen, Entropy for group endomorphism and homogeneous space, Trans. Amer. Math. Soc, 153 (1971), 401-414.   DOI
8 Ch. Corda, M. Fatehi Nia, M. R. Molaei and Y. Sayyari, Entropy of iterated function systems and their relations with black holes and bohr-like black holes entropies, Entropy, 20 (2018), 56-72.   DOI
9 Cuomo, M. Kevin and Alan V. Oppenheim, Chaotic signals and systems for communications, IEEE International Conference on Acoustics, (1993).
10 X. Dai, Z. Zhou and X. Geng., Some Relations between Hausdorff-dimensions and Entropies, J. Sci. China Ser. A, 41 (1998), 1068-1075.   DOI
11 E. I. Dinaburg, On the Relations Among Various Entropy Characteristics of Dynamical Systems, Math. USSR Izv, 5 (1971), 337-378.   DOI
12 O. Garasym, J. P. Lozi, and R. Lozi, How useful randomness for cryptography can emerge from multicore-implemented complex networks of chaotic maps. J. Difference Equ, Appl, 23 (2017), 821-859.   DOI
13 M. Misiurewicz, W. Szlenk, Entropy of Piecewise Monotone Mappings, Asterisque, 50 (1978), 299-310.
14 T. N. T. Goodman, Z. Jinlian and H. Lianfa, Relating Topological Entropy and Measure Entropy, Bull. Lond. Math, 43 (1971), 176-180.
15 S. Ito, An Estimate from above for the Entropy and the Topological Entropy of a C1-diffeomorphism, Proc. Japan Acad, 46 (1970), 226-230.   DOI
16 S. Ito, On the Topological Entropy of a Dynamical System, Proc. Japan Acad, 4 (1969), 838-840.   DOI
17 Khalil. H, Nonlinear control, New York Pearson, (2015).
18 M. J. Lee, Introduction to smooth manifolds, GTM, 218 (2002).
19 Nitecki and H. Zbigniew, Topological entropy and the preimage structure of maps, Real Anal. Exchange, 29 (2003/04), 9-41.   DOI
20 Ogata, Katsuhiko, and Yanjuan Yang, Modern control engineering, Prentice-Hall(2002).
21 M. Patrao, Entropy and its variational principle for noncompact metric space, Ergodic Theory and Dynamical Systems, 30 (2010), 1529-1542.   DOI
22 Thomson, William, Theory of vibration with applications, CrC Press. (2018).
23 V. Volterra, Theory of functionals and of integral and integro-differential equations, Courier Corporation, 2005.
24 Y. Zhu, Z. Jinlian and H. Lianfa , Topological entropy of a sequence of monotone maps on circles, J. Korean Math. Soc. 43 (2006), 373-382.   DOI