It is shown that f has a periodic point with period not a power of 2, if and only if there is a chain reccurent point x of f, such that x is asymptotically periodic but non-periodic.

• 本文证明了f有周期为非2方幂的周期点,当且仅当存在f的链回归点x,使得x是渐近周期点但不是周期点。