Scrambled sets of shift operators
-
1506
Downloads
-
2180
Views
Authors
Xinxing Wu
- School of Sciences, Southwest Petroleum University, Chengdu, Sichuan, 610500, People's Republic of China.
Guanrong Chen
- Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, People's Republic of China.
Abstract
In this paper, some characterizations about orbit invariants, p-scrambled points and scrambled sets are
obtained. Applying these results solves a conjecture and two problems given in [X. Fu, Y. You, Nonlinear
Anal., 71 (2009), 2141-2152].
Share and Cite
ISRP Style
Xinxing Wu, Guanrong Chen, Scrambled sets of shift operators, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 2631--2637
AMA Style
Wu Xinxing, Chen Guanrong, Scrambled sets of shift operators. J. Nonlinear Sci. Appl. (2016); 9(5):2631--2637
Chicago/Turabian Style
Wu, Xinxing, Chen, Guanrong. "Scrambled sets of shift operators." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 2631--2637
Keywords
- Li-Yorke chaos
- scrambled (chaotic) set
- shift operator.
MSC
References
-
[1]
E. Akin, Recurrence in Topological Dynamical Systems, Families and Ellis Actions, The University Series in Mathematics, Plenum Press, New York (1997)
-
[2]
X. Fu, Z. Chen, H. Gao, C. Li, Z. Liu, Chaotic sets of continuous and discontinuous maps, Nonlinear Anal., 72 (2010), 399-408.
-
[3]
X. Fu, Y. You, Chaotic sets of shift and weighted shift maps, Nonlinear Anal., 71 (2009), 2141-2152.
-
[4]
Y. Lan, Chaos in nonautonomous discrete fuzzy dynamical systems, J. Nonlinear Sci. Appl., 9 (2016), 404-412.
-
[5]
T. Y. Li, J. A. Yorke, Period three implies chaos, Amer. Math. Monthly, 82 (1975), 985-992.
-
[6]
P. Oprocha, P. WilczyĆki, Shift spaces and distributional chaos, Chaos Solitons Fractals, 31 (2007), 347-355.
-
[7]
R. Piku la, On some notions of chaos in dimension zero, Colloq. Math., 107 (2007), 167-177.
-
[8]
B. Schweizer, J. Smítal, Measures of chaos and a spectral decomposition of dynamical systems on the interval, Trans. Amer. Math. Soc., 344 (1994), 737-754.
-
[9]
J. Smítal, M. Štefánková , Distributional chaos for triangular maps, Chaos Solitons Fractals, 21 (2004), 1125-1128.
-
[10]
X. Wu, G. Chen, On the large deviations theorem and ergodicity, Commun. Nonlinear Sci. Numer. Simul., 30 (2016), 243-247.
-
[11]
X. Wu, J. Wang, G. Chen, F-sensitivity and multi-sensitivity of hyperspatial dynamical systems, J. Math. Anal. Appl., 429 (2015), 16-26.
-
[12]
X. Wu, P. Zhu, Invariant scrambled set and maximal distributional chaos, Ann. Polon. Math., 109 (2013), 271- 278.
-
[13]
X. Ye, R. Zhang, On sensitive sets in topological dynamics, Nonlinearity, 21 (2008), 1601-1620.