A note about various types of sensitivity in general semiflows

Abstract

<p>We discuss the implications between various types of sensitivity in general semiflows (sensitivity, syndetic sensitivity, thick sensitivity, thick syndetic sensitivity, multisensitivity, periodic sensitivity, thick periodic sensitivity), including the weak mixing as a very strong type of sensitivity and the strong mixing as the strongest of all type of sensitivity.</p>

A note on the sensitivity of semiflows

“…Then, they [12] generalized some results on chaotic properties of cascades to the product of semiflows and asked the following question. (For more recent results on sensitivity, refer to [2,4,5,7,8,9,10,17,18,19,21,22] and some references therein.) Question 1.…”

“…Recently, Miller [10] discussed relations between various types of sensitivity in general semiflows and asked the following question: Let L 0 = L 0 = 0, L 1 = L 1 = 2, and L n = 2 L1+···+Ln−1 ·(2n), L n = L 1 +L 2 +· · ·+L n for all n ≥ 2, and set…”

“…[13, Open question 3] Let (G, X) be a sensitive semiflow and G 1 be a syndetic closed submonoid of G. Is (G 1 , X) necessarily sensitive? Recently, Miller [10] discussed relations between various types of sensitivity in general semiflows and asked the following question:…”