On $ n $-tuplewise IP-sensitivity and thick sensitivity

Let $(X,T)$ be a topological dynamical system and $n\geq 2$. We say that is $n$-tuplewise IP-sensitive (resp. thickly sensitive) if there exists constant $\delta>0$ with the property for each non-empty open subset $U$ of $X$, exist $x_1,x_2,\dotsc,x_n\in U$ such \[ \Bigl\{k\in\mathbb{N}\colon \min_{1\le i\delta\Bigr\} \] an IP-set thick set). obtain several sufficient necessary conditions to or sensitive show any non-trivial weakly mixing all 2$, while it only has at least $n$ minimal points. characterize two kinds sensitivity by considering some kind factor maps. introduce opposite side pairwise IP-sensitivity sensitivity, named (almost) IP$^*$-equicontinuity syndetic equicontinuity, dichotomies results them. In particular, we distal IP$^*$-equicontinuous. every admits maximal almost IP$^*$-equicontinuous equicontinuous factor, them maps their factors.