Multi-separation, centrifugality and centripetality imply chaos

Author:
Jiehua Mai

Journal:
Trans. Amer. Math. Soc. **351** (1999), 343-351

MSC (1991):
Primary 58F03; Secondary 58F13, 26A18

MathSciNet review:
1473450

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be an interval. need not be compact or bounded. Let be a continuous map, and be a trajectory of with or . Then there is a point such that . A point is called a centripetal point of relative to if or , and is centrifugal if or . In this paper we prove that if there exist centripetal points of in , then has periodic points of some odd () period . In addition, we also prove that if ) is multi-separated by Fix(), or there exists a centrifugal point of in , then is turbulent and hence has periodic points of all periods.

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Additional Information

**Jiehua Mai**

Affiliation:
Institute of Mathematics, Shantou University, Shantou, Guangdong 515063 P. R. China

Email:
jhmai@mailserv.stu.edu.cn

DOI:
https://doi.org/10.1090/S0002-9947-99-02191-1

Keywords:
Return trajectory,
centripetal point,
centrifugal point,
period,
turbulence,
chaos

Received by editor(s):
January 30, 1997

Additional Notes:
This research was supported by the National Natural Science Foundation of China

Article copyright:
© Copyright 1999
American Mathematical Society