The Neighbourhood Sensitivity In The Interval Map And The Discussing Of The Attractor's Definition

This paper is composed of two parts: the neighborhood sensitivity in the interval map; the discussing about the definition of the attractor. In the first part, under the Devaney chaos, we give a new definition of sensitivity, called neighborhood sensitivity. This is a more strict definition. We also proof that they are equal on the interval map. In the second part, we compare the Milnor's definition of the attractor with the others. And through discussing the attractors of some simple examples, we can draw the conclusion that Milnor's definition can be more widely used.