数学物理学报(英文版) ›› 2004, Vol. 24 ›› Issue (4): 698-704.

• 论文 • 上一篇    

THE ASYMPTOTIC PERIODICITY OF PIECEWISE MONOTONE SELFMAPS OF THE INTERVAL

 丁义明   

  1. Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071, China
  • 出版日期:2004-10-20 发布日期:2004-10-20
  • 基金资助:

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

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)

摘要:

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

关键词: Interval map, asymptotically periodic, derived set

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

中图分类号: 

  • 37D05