The multi-\(\mathbb{F}\)-sensitivity and \((\mathbb{F}_1, \mathbb{F}_2)\)-sensitivity for product systems

Volume 9, Issue 6, pp 4364--4370 http://dx.doi.org/10.22436/jnsa.009.06.76

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Authors

Xinxing Wu - School of Sciences, Southwest Petroleum University, Chengdu, Sichuan, 610500, P. R. China. Risong Li - School of Science, Guangdong Ocean University, Zhanjiang, Guangdong, 524025, P. R. China. Yiran Zhang - School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, P. R. China.

Abstract

In this paper, it is proved that the product system \((X \times Y; T \times S)\) is multi-\(\mathbb{F}\)-sensitive (resp., \((\mathbb{F}_1, \mathbb{F}_2)\)- sensitive) if and only if \((X; T)\) or \((Y; S)\) is multi-F-sensitive (resp., \((\mathbb{F}_1, \mathbb{F}_2)\)-sensitive) when Furstehberg families \(\mathbb{F}\) and \(\mathbb{F}_2\) have the Ramsey property, improving the main results in [N. Değirmenci, Ş. Koçak, Turk. J. Math., 34 (2010), 593-600] and [R. Li, X. Zhou, Turk. J. Math., 37 (2013), 665-675]. Moreover, some analogical results for semi- flows are obtained.

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Keywords

• Multi-\(\mathbb{F}\)-sensitivity
• \((\mathbb{F}_1، \mathbb{F}_2)\)-sensitivity
• Li-Yorke sensitivity
• product system.

MSC

•  54H20
•  54B20
•  37B99
•  37D45

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