Classification of Maps on Intervals That Exhibit Dense Periodic Points

Abstract

In this paper, continuous maps on interval with dense set of periodic points such that the periods being set of natural numbers are studied.These maps named as Peri- odically Rich maps could be divided into two classes on Interval, such as the maps with period four points having increasing periodic orbit and the maps with two fixed points such that image of a subset of Interval does not belong to the same subset. Notion of bigness of Periodically Rich maps is also discussed.