数学物理学报(英文版) ›› 1999, Vol. 19 ›› Issue (1): 114-120.

• 论文 • 上一篇    

THE ASYMPTOTIC PERIODICITY OF LORENZ MAPS

 丁义明, 范文涛   

  1. Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071, China
  • 收稿日期:1998-03-12 出版日期:1999-03-02 发布日期:1999-03-02
  • 基金资助:

    This work is partially supported by the NSFC (69874039)

THE ASYMPTOTIC PERIODICITY OF LORENZ MAPS

 DING Xi-Meng, FAN Wen-Chao   

  1. Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071, China
  • Received:1998-03-12 Online:1999-03-02 Published:1999-03-02
  • Supported by:

    This work is partially supported by the NSFC (69874039)

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摘要：

Lorenz map f : I ! I is a one dimensional piecewise monotone map with
a single discontinuity c. Let C(f) = [
n≥0
f−n(c) be the collection of all the preimages of c.
Authors prove that if C′(f) is countable then there exists M such that Card(!(x))  M
for all x 2 I. If C′(f) is uncountable then !(x) is uncountable for some x 2 I. So f is
asymptotically periodic if and only if C′(f) is countable.

关键词: Lorenz map, critical point, derived set, asymptotically periodic, renormalization.

Abstract:

Lorenz map f : I ! I is a one dimensional piecewise monotone map with
a single discontinuity c. Let C(f) = [
n≥0
f−n(c) be the collection of all the preimages of c.
Authors prove that if C′(f) is countable then there exists M such that Card(!(x))  M
for all x 2 I. If C′(f) is uncountable then !(x) is uncountable for some x 2 I. So f is
asymptotically periodic if and only if C′(f) is countable.

Key words: Lorenz map, critical point, derived set, asymptotically periodic, renormalization.

中图分类号: 

  • 58F03
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