Pesin topological entropy of nonautonomous dynamical systems. (English) Zbl 1465.37023
Summary: This paper studies the dynamical properties of Pesin topological entropy for nonautonomous dynamical systems which was proposed by Z. Li [Int. J. Bifurcation Chaos Appl. Sci. Eng. 25, No. 12, Article ID 1550158, 5 p. (2015; Zbl 1328.37011)]. Furthermore, it is showed that if the sequence is constituted by locally expanding or Lipschitz maps with the same expanding or Lipschitz constant \(L > 1\), then the box dimension of any subset multiplied by the logarithm of the expanding or Lipschitz constant \(L\) give a lower and upper bound of the corresponding Pesin topological entropies on the subset.
Citations:
Zbl 1328.37011References:
| [1] | Adler, R.; Konheim, A.; McAndrew, M., Topological entropy, Trans. Am. Math. Soc., 114, 309-319 (1965) · Zbl 0127.13102 |
| [2] | Biś, A., Topological and measure-theoretical entropies of nonautonomous dynamical systems, J. Dyn. Differ. Equ., 30, 273-285 (2018) · Zbl 1407.37025 |
| [3] | Biś, A.; Namiecińska, A., Hausdorff dimension and topological entropies of a solenoid, Entropy, 22, 506 (2020), 16 pp. |
| [4] | Bowen, R., Entropy for group endomorphisms and homogeneous spaces, Trans. Am. Math. Soc., 153, 401-414 (1971) · Zbl 0212.29201 |
| [5] | Bowen, R., Topological entropy for noncompact sets, Trans. Am. Math. Soc., 184, 125-136 (1973) · Zbl 0274.54030 |
| [6] | Dai, X.; Jiang, Y., Distance entropy of dynamical systems on noncompact-phase spaces, Discrete Contin. Dyn. Syst., 20, 313-333 (2007) · Zbl 1144.37004 |
| [7] | Dai, X.; Zhou, Z.; Geng, X., Some relations between Hausdorff-dimensions and entropies, Sci. China Ser. A, 41, 1068-1075 (1998) · Zbl 0918.58039 |
| [8] | Dinaburg, E. I., The relation between topological entropy and metric entropy, Sov. Math. Dokl., 11, 13-16 (1970) · Zbl 0196.26401 |
| [9] | Huang, X.; Wen, X.; Zeng, F., Topological pressure of nonautonomous dynamical systems, Nonlinear Dyn. Syst. Theory, 8, 43-48 (2008) · Zbl 1300.37007 |
| [10] | Ju, Y.; Ma, D.; Wang, Y., Topological entropy of free semigroup actions for noncompact sets, Discrete Contin. Dyn. Syst., 39, 995-1017 (2019) · Zbl 1417.37082 |
| [11] | Kawan, C., Metric entropy of nonautonomous dynamical systems, Nonauton. Stoch. Dyn. Syst., 1, 26-52 (2013) · Zbl 1372.37041 |
| [12] | Kolyada, S.; Misiurewicz, M.; Snoha, Ł., Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval, Fundam. Math., 160, 161-181 (1999) · Zbl 0936.37004 |
| [13] | Kolyada, S.; Snoha, Ł., Topological entropy of nonautonomous dynamical systems, Random Comput. Dyn., 4, 205-233 (1996) · Zbl 0909.54012 |
| [14] | Kolyada, S.; Snoha, Ł.; Trofimchuk, S., On minimality of nonautonomous dynamical systems, Nonlinear Oscil., 7, 83-89 (2004) · Zbl 1092.37011 |
| [15] | Kong, M.; Cheng, W.; Li, B., Topological pressure for nonautonomous systems, Chaos Solitons Fractals, 76, 82-92 (2015) · Zbl 1352.37052 |
| [16] | Kuang, R.; Cheng, W.; Li, B., Fractal entropy of nonautonomous systems, Pac. J. Math., 262, 421-436 (2013) · Zbl 1384.37012 |
| [17] | Li, Z., Remarks on topological entropy of nonautonomous dynamical systems, Int. J. Bifurc. Chaos, 25, 155-158 (2015) · Zbl 1328.37011 |
| [18] | Li, Z.; Zhang, W.; Wang, W., Topological entropy dimension for nonautonomous dynamical systems, J. Math. Anal. Appl., 475, 1978-1991 (2019) · Zbl 1410.37017 |
| [19] | Ma, D.; Cai, B., Topological entropy of proper map, Taiwan. J. Math., 18, 1219-1241 (2014) · Zbl 1357.37008 |
| [20] | Ma, D.; Wu, M., On Hausdorff dimension and topological entropy, Fractals, 18, 363-370 (2010) · Zbl 1206.28008 |
| [21] | Ma, D.; Wu, M., Topological pressure and topological entropy of a semigroup of maps, Discrete Contin. Dyn. Syst., 31, 545-557 (2011) · Zbl 1234.37011 |
| [22] | Ma, J.; Wen, Z., A Billingsley type theorem for Bowen entropy, C. R. Math. Acad. Sci. Paris, 346, 503-507 (2008) · Zbl 1138.37007 |
| [23] | Misiurewicz, M., On Bowen definition of topological entropy, Discrete Contin. Dyn. Syst., 10, 827-833 (2004) · Zbl 1056.37016 |
| [24] | Pesin, Y., Dimension Theory in Dynamical Systems (1997), University of Chicago Press: University of Chicago Press Chicago |
| [25] | Pesin, Y.; Pitskel’, B. S., Topological pressure and the variational principle for noncompact sets, Funkc. Anal. Prilozh., 18, 50-63 (1984), (in Russian) · Zbl 0567.54027 |
| [26] | Ruelle, D., Thermodynamic Formalism (1978), Addison-Wesley · Zbl 0401.28016 |
| [27] | Walters, P., An Introduction to Ergodic Theory (1982), Springer-Verlag: Springer-Verlag New York, Heidelberg, Berlin · Zbl 0475.28009 |
| [28] | Xu, L.; Zhou, X., Variational principles for entropies of nonautonomous dynamical systems, J. Dyn. Differ. Equ., 30, 1053-1062 (2017) · Zbl 1401.37011 |
| [29] | Zhao, Y.; Pesin, Y., Scaled entropy for dynamical systems, J. Stat. Phys., 158, 447-475 (2015) · Zbl 1360.37048 |
| [30] | Zhu, Y.; Liu, Z.; Xu, X.; Zhang, W., Entropy of nonautonomous dynamical systems, J. Korean Math. Soc., 49, 165-185 (2012) · Zbl 1252.37009 |
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