Unpredictable points and chaos

•Unpredictable points are introduced on the basis of Poisson stability.•A chaos is proved in a quasi-minimal set with an unpredictable point.•The chaos is initiated from a single motion characteristics.•The chaos is with sensitivity and an uncountable set of dense Poisson stable orbits.•The symbolic dynamics illustrates all the results.

It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. The existing definitions of chaos are formulated in sets of motions. This is the first time in the literature that description of chaos is initiated from a single motion. The theoretical results are exemplified by means of the symbolic dynamics.