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

Volume 9, Issue 11, pp 5772--5779 http://dx.doi.org/10.22436/jnsa.009.11.06

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Authors

Cuina Ma - School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, P. R. China. Peiyong Zhu - School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, P. R. China. Risong Li - School of Science, Guangdong Ocean University, Zhanjiang, Guangdong, 524025, P. R. China.

Abstract

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.

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Keywords

• Non-autonomous discrete system
• Furstenberg family
• \((\mathcal{F}_1،\mathcal{F}_2)\)-sensitivity
• weak \((\mathcal{F}_1،\mathcal{F}_2)\)- sensitivity.

MSC

•  54H20
•  54B20
•  37B99
•  37D45

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