On iteration invariants for \((\mathcal{F}_1,\mathcal{F}_2)\)sensitivity and weak \((\mathcal{F}_1,\mathcal{F}_2)\)sensitivity of nonautonomous discrete systems

In this paper, let \((X; f_{1;\infty})\) be a nonautonomous 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 \(k gt; 0\). 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.