Relativization of sensitivity in minimal systems

Let V. X; T /!.Y; S / be an extension between minimal systems; we consider its relative sensitivity. We obtain that is relatively n-sensitive if and only if the relative n-regionally proximal relation contains a point whose coordinates are distinct; and the structure of which is relatively n-sensitive but not relatively.n C 1/-sensitive is determined. Let F t be the families consisting of thick sets. We introduce notions of relative block F t -sensitivity and relatively strong F t -sensitivity. Let V. X; T /!.Y; S / be an extension between minimal systems. Then the following Auslander-Yorke type dichotomy theorems are obtained: (1) is either relatively block Ft -sensitive or V. X; T /!. X eq; Teq / is a proximal extension where. X eq; Teq /!.Y; S / is the maximal equicontinuous factor of . (2) is either relatively strongly Ft -sensitive or V. X; T /!. X d; Td / is a proximal extension where. X d; Td /!.Y; S / is the maximal distal factor of