Research on quasi-weakly almost periodic point

We study sensitivities and shadowing property of two binary sub-shifts. We show that the first one is collectively sensitive, multi-sensitive and thickly syndetically sensitive but not Li–Yorke sensitive or cofinite sensitive or chain mixing, while the second one is not only collectively sensitive, multi-sensitive and thickly syndetically sensitive but also Li–Yorke sensitive and cofinite sensitive. Neither those two binary sub-shifts have shadowing property. These results suggest that there are differences and also similarities between these two sub-shifts. Also, these results show Devaney chaos + Kato chaos + thickly syndetic sensitivity + multi-sensitivity + collective sensitivity doesn't imply any one of Li–Yorke sensitivity, cofinite sensitivity, weakly mixing or chain mixing, and exact doesn't imply shadowing property.