Geodesic
On iteration invariants for $(\mathcal{F}_1,\mathcal{F}_2)$-sensitivity and weak $(\mathcal{F}_1,\mathcal{F}_2)$-sensitivity of non-autonomous discrete systems
Ma, Cuina1 ; Zhu, Peiyong1 ; Li, Risong2
1 School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, P. R. China
2 School of Science, Guangdong Ocean University, Zhanjiang, Guangdong, 524025, P. R. China
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 11, p. 5772-5779.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, let $(X; f_{1;\infty})$ be a non-autonomous discrete system on a compact metric space $X$. For a positive k, the properties $\hat{P}(k)$ and $\hat{Q}(k)$ of Furstenberg families are introduced for any integer $k > 0$. Based on the two properties, we prove that $(\mathcal{F}_1,\mathcal{F}_2)$-sensitivity and weak $(\mathcal{F}_1,\mathcal{F}_2)$-sensitivity are inherited under iterations.
DOI : 10.22436/jnsa.009.11.06
Classification : 54H20, 54B20, 37B99, 37D45
Keywords: Non-autonomous discrete system, Furstenberg family, \((\mathcal{F}_1،\mathcal{F}_2)\)-sensitivity, weak \((\mathcal{F}_1،\mathcal{F}_2)\)- sensitivity.

Ma, Cuina 1 ; Zhu, Peiyong 1 ; Li, Risong 2

1 School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, P. R. China
2 School of Science, Guangdong Ocean University, Zhanjiang, Guangdong, 524025, P. R. China 
@article{JNSA_2016_9_11_a5,
     author = {Ma, Cuina and Zhu, Peiyong and Li, Risong},
     title = {On iteration invariants for {\((\mathcal{F}_1,\mathcal{F}_2)\)-sensitivity} and weak {\((\mathcal{F}_1,\mathcal{F}_2)\)-sensitivity} of non-autonomous discrete systems},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {5772-5779},
     publisher = {mathdoc},
     volume = {9},
     number = {11},
     year = {2016},
     doi = {10.22436/jnsa.009.11.06},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.11.06/}
}
TY  - JOUR
AU  - Ma, Cuina
AU  - Zhu, Peiyong
AU  - Li, Risong
TI  - On iteration invariants for \((\mathcal{F}_1,\mathcal{F}_2)\)-sensitivity and weak \((\mathcal{F}_1,\mathcal{F}_2)\)-sensitivity of non-autonomous discrete systems
JO  - Journal of nonlinear sciences and its applications
PY  - 2016
SP  - 5772
EP  - 5779
VL  - 9
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.11.06/
DO  - 10.22436/jnsa.009.11.06
LA  - en
ID  - JNSA_2016_9_11_a5
ER  - 
%0 Journal Article
%A Ma, Cuina
%A Zhu, Peiyong
%A Li, Risong
%T On iteration invariants for \((\mathcal{F}_1,\mathcal{F}_2)\)-sensitivity and weak \((\mathcal{F}_1,\mathcal{F}_2)\)-sensitivity of non-autonomous discrete systems
%J Journal of nonlinear sciences and its applications
%D 2016
%P 5772-5779
%V 9
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.11.06/
%R 10.22436/jnsa.009.11.06
%G en
%F JNSA_2016_9_11_a5
Ma, Cuina; Zhu, Peiyong; Li, Risong. On iteration invariants for \((\mathcal{F}_1,\mathcal{F}_2)\)-sensitivity and weak \((\mathcal{F}_1,\mathcal{F}_2)\)-sensitivity of non-autonomous discrete systems. Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 11, p. 5772-5779. doi : 10.22436/jnsa.009.11.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.11.06/

[1] Akin, E. Recurrence in topological dynamics, Furstenberg families and Ellis actions, The University Series in Mathematics, Plenum Press, New York, 1997

[2] Akin, E.; Kolyada, S. Li-Yorke sensitivity, Nonlinearity, Volume 16 (2003), pp. 1421-1433

[3] Elaydi, S. N. Nonautonomous difference equations: open problems and conjectures, Differences and differential equations, Fields Inst. Commun., Amer. Math. Soc., Providence, RI, Volume 42 (2004), pp. 423-428

[4] Elaydi, S.; Sacker, R. J. Nonautonomous Beverton-Holt equations and the Cushing-Henson conjectures, J. Difference Equ. Appl., Volume 11 (2005), pp. 337-346

[5] Glasner, E.; Weiss, B. Sensitive dependence on initial conditions, Nonlinearity, Volume 6 (1993), pp. 1067-1075

[6] Huang, Q. L.; Shi, Y. M.; Zhang, L. J. Sensitivity of non-autonomous discrete dynamical systems, Appl. Math. Lett., Volume 39 (2015), pp. 31-34

[7] Kolyada, S.; Misiurewicz, M.; Snoha, L. Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval, Fund. Math., Volume 160 (1999), pp. 161-181

[8] Kolyada, S.; Snoha, L. Topological entropy of nonautonomous dynamical systems, Random Comput. Dynam., Volume 4 (1996), pp. 205-233

[9] Li, R. S. A note on chaos via Furstenberg family couple, Nonlinear Anal., Volume 72 (2010), pp. 2290-2299

[10] Li, R. S. A note on stronger forms of sensitivity for dynamical systems, Chaos Solitons Fractals, Volume 45 (2012), pp. 753-758

[11] Li, R. S. The large deviations theorem and ergodic sensitivity, Commun. Nonlinear Sci. Numer. Simul., Volume 18 (2013), pp. 819-825

[12] Li, R. S.; Shi, Y. M. Several sufficient conditions for sensitive dependence on initial conditions, Nonlinear Anal., Volume 72 (2010), pp. 2716-2720

[13] Li, Z. H.; Wang, H. Y.; Xiong, J. C. Some remarks on (\(F_1;F_2\))-scrambled sets, (Chinese) Acta Math. Sinica (Chin. Ser.), Volume 53 (2010), pp. 727-732

[14] Li, R. S.; Zhou, X. L. A note on chaos in product maps, Turkish J. Math., Volume 37 (2013), pp. 665-675

[15] Moothathu, T. K. S. Stronger forms of sensitivity for dynamical systems, Nonlinearity, Volume 20 (2007), pp. 2115-2126

[16] Shao, S.; Ye, X. D.; Zhang, R. F. Sensitivity and regionally proximal relation in minimal systems, Sci. China Ser. A, Volume 51 (2008), pp. 987-994

[17] Tan, F.; Xiong, J. C. Chaos via Furstenberg family couple, Topology Appl., Volume 156 (2009), pp. 525-532

[18] Tan, F.; Zhang, R. F. On F-sensitive pairs, Acta Math. Sci. Ser. B Engl. Ed., Volume 31 (2011), pp. 1425-1435

[19] Wu, X. X.; Chen, G. R. On the large deviations theorem and ergodicity, Commun. Nonlinear Sci. Numer. Simul., Volume 30 (2016), pp. 243-247

[20] Wu, X. X.; Chen, G. R.; Zhu, P. Y. On weak Lyapunov exponent and sensitive dependence of interval maps, Internat. J. Bifur. Chaos Appl. Sci. Engrg., Volume 24 (2014), pp. 1-5

[21] Wu, X. X.; Oprocha, P.; Chen, G. R. On various definitions of shadowing with average error in tracing, Nonlinearity, Volume 29 (2016), pp. 1942-1972

[22] Wu, X. X.; Wang, X. On the iteration properties of large deviations theorem, Internat. J. Bifur. Chaos Appl. Sci. Engrg., Volume 26 (2016), pp. 1-6

[23] Wu, X. X.; Wang, X.; Chen, G. R. F-mixing property and (F1, F2)-everywhere chaos of inverse limit dynamical systems, Nonlinear Anal., Volume 104 (2014), pp. 147-155

[24] Wu, X. X.; Wang, J. J.; Chen, G. R. F-sensitivity and multi-sensitivity of hyperspatial dynamical systems, J. Math. Anal. Appl., Volume 429 (2015), pp. 16-26

[25] Wu, X. X.; Wang, L. D.; Chen, G. R. Weighted backward shift operators with invariant distributionally scrambled subsets, Ann. Funct. Anal. ((accepted))

[26] Wu, X. X.; Zhu, P. Y. Chaos via a couple of Furstenberg families, (Chinese) Acta Math. Sinica (Chin. Ser.), Volume 55 (2012), pp. 1039-1054

[27] Wu, X. X.; Zhu, P. Y. Chaos in a class of non-autonomous discrete systems, Appl. Math. Lett., Volume 26 (2013), pp. 432-436

[28] Xiong, J. C. Chaos in a topologically transitive system, Sci. China Ser. A, Volume 48 (2005), pp. 929-939

[29] Ye, X. D.; Zhang, R. F. On sensitive sets in topological dynamics, Nonlinearity, Volume 21 (2008), pp. 1601-1620

Cité par Sources :