THE VARIATIONAL PRINCIPLE FOR THE PACKING ENTROPY OF NONAUTONOMOUS DYNAMICAL SYSTEMS

  • Ruifeng ZHANG ,
  • Jianghui ZHU
Expand
  • School of Mathematics, Hefei University of Technology, Hefei 230009, China

Received date: 2022-04-06

  Revised date: 2022-08-25

  Online published: 2023-08-08

Supported by

National Natural Science Foundation of China (11871188, 12031019).

Abstract

Let $(X,\phi)$ be a nonautonomous dynamical system. In this paper, we introduce the notions of packing topological entropy and measure-theoretical upper entropy for nonautonomous dynamical systems. Moreover, we establish the variational principle between the packing topological entropy and the measure-theoretical upper entropy.

Cite this article

Ruifeng ZHANG , Jianghui ZHU . THE VARIATIONAL PRINCIPLE FOR THE PACKING ENTROPY OF NONAUTONOMOUS DYNAMICAL SYSTEMS[J]. Acta mathematica scientia, Series B, 2023 , 43(4) : 1915 -1924 . DOI: 10.1007/s10473-023-0426-7

References

[1] Adler R L, Konheim A G, McAndrew M H. Topological entropy. Trans Amer Math Soc, 1965, 114: 309-319
[2] Biś A. Topological and measure-theoretical entropies of nonautonomous dynamical systems. J Dynam Differential Equations, 2018, 30(1): 273-285
[3] Bowen R. Topological entropy for noncompact sets. Trans Amer Math Soc, 1973, 184: 125-136
[4] Dinaburg E I. A correlation between topological entropy and metric entropy. Dokl Akad Nauk SSSR, 1970, 190: 19-22
[5] Dou D, Zheng D, Zhou X.Packing topological entropy for amenable group actions. Ergodic Theory Dynam Systems, 2021. DOI:10.1017/etds.2021.126
[6] Feng D, Huang W. Variational principles for topological entropies of subsets. J Funct Anal, 2012, 263(8): 2228-2254
[7] Goodman T N T. Relating topological entropy and measure entropy. Bull London Math Soc, 1971, 3(2): 176-180
[8] Goodwyn L W. Topological entropy bounds measure-theoretic entropy. Proc Amer Math Soc, 1969, 23: 679-688
[9] Huang X, Wen X, Zeng F. Topological pressure of nonautonomous dynamical systems. Nonlinear Dyn Syst Theory, 2008, 8(1): 43-48
[10] Jech T. Set Theory. Berlin: Springer, 2003
[11] Ju Y, Yang Q. Pesin topological entropy of nonautonomous dynamical systems. J Math Anal Appl, 2021, 500(2): 125125
[12] Kawan C. Metric entropy of nonautonomous dynamical systems. Nonauton Dyn Syst, 2014, 1(1): 26-52
[13] Kolmogorov A N. A new metric invariant of transient dynamical systems and automorphisms in Lebesgue spaces. Dokl Akad Nauk SSSR (Russian), 1958, 119: 861-864
[14] Kolyada S, Snoha L. Topological entropy of nonautonomous dynamical systems. Random Comput Dynam, 1996, 4(2/3): 205-233
[15] Kuang R, Cheng W, Li B. Fractal entropy of nonautonomous systems. Pacific J Math, 2013, 262(2): 421-436
[16] Li Z, Zhang W, Wang W. Topological entropy dimension for nonautonomous dynamical systems. J Math Anal Appl, 2019, 475(2): 1978-1991
[17] Liu K, Qiao Y, Xu L. Topological entropy of nonautonomous dynamical systems. J Differential Equations, 2020, 268(9): 5353-5365
[18] Mattila P.Geometry of Sets and Measures in Euclidean Spaces. Cambridge: Cambridge University Press, 1995
[19] Xu L, Zhou X. Variational principles for entropies of nonautonomous dynamical systems. J Dynam Differential Equations, 2018, 30(3): 1053-1062
[20] Zhou X, Chen E, Cheng W. Packing entropy and divergence points. Dyn Syst, 2012, 27(3): 387-402
[21] Zhu Y, Liu Z, Xu X, Zhang W. Entropy of nonautonomous dynamical systems. J Korean Math Soc, 2012, 49(1): 165-185
Options
Outlines

/