  In this paper we study several stronger forms of sensitivity for continuous
surjective selfmaps on compact metric spaces and relations between them. The
main result of the paper states that a minimal system is either multi-sensitive
or an almost one-to-one extension of its maximal equicontinuous factor, which
is an analog of the Auslander-Yorke dichotomy theorem. For minimal dynamical
systems, we also show that all notions of thick sensitivity, multi-sensitivity
and thickly syndetical sensitivity are equivalent, and all of them are much
stronger than sensitivity.

Dynamical Systems