Acta mathematica scientia,Series B ›› 2004, Vol. 24 ›› Issue (4): 698-704.

• Articles • Previous Articles    

THE ASYMPTOTIC PERIODICITY OF PIECEWISE MONOTONE SELFMAPS OF THE INTERVAL

 DING Yi-Ming   

  1. Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071, China
  • Online:2004-10-20 Published:2004-10-20
  • Supported by:

    This work is partially supported by the NSFC (No.60174048,70271076)

Abstract:

Let f : I ! I be a piecewise monotone interval map. The critical point set C(f) of f consists of all the preimages of its turning points. It is proved that the
complex dynamical behaviors of f are all concentrated on the derived set of C(f). f is asymptotically periodic if and only if the derived set of C(f) is countable

Key words: Interval map, asymptotically periodic, derived set

CLC Number: 

  • 37D05
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