ABUNDANCE OF UNIMODAL MAPS WITH DENSE CRITICAL ORBIT AND PREFIXED CRITICAL ORBIT

Applied Mathematics and Mechanics (English Edition) ›› 2000, Vol. 21 ›› Issue (4): 389-394.

ABUNDANCE OF UNIMODAL MAPS WITH DENSE CRITICAL ORBIT AND PREFIXED CRITICAL ORBIT

曹永罗¹, 王兰宇²

1. Department of Mathematics, Suzhou University, Suzhou 215006, P. R. China;
2. Institute of Mathematics, Academia Sinica, Beijing 100080, P. R. China

收稿日期:1998-11-20 修回日期:1999-10-18 出版日期:2000-04-18 发布日期:2000-04-18
基金资助:
the National Natural Science Foundation of China (19501030)

ABUNDANCE OF UNIMODAL MAPS WITH DENSE CRITICAL ORBIT AND PREFIXED CRITICAL ORBIT

Cao Yongluo¹, Wang Lanyu²

1. Department of Mathematics, Suzhou University, Suzhou 215006, P. R. China;
2. Institute of Mathematics, Academia Sinica, Beijing 100080, P. R. China

Received:1998-11-20 Revised:1999-10-18 Online:2000-04-18 Published:2000-04-18
Supported by:
the National Natural Science Foundation of China (19501030)

摘要/Abstract

摘要： For the so-called quadratic family, it is proved that, there exists a positive Lebesgue measure set E in the parameter space such that the corresponding map has a dense critical orbit in the support set of the invariant measure for almost all parameters in E; it is also proved that there is a dense set in E such that the critical orbit of the corresponding map enter the reversed fixed point.

关键词: unimodal map, quadratic family, invariant measure

Abstract: For the so-called quadratic family, it is proved that, there exists a positive Lebesgue measure set E in the parameter space such that the corresponding map has a dense critical orbit in the support set of the invariant measure for almost all parameters in E; it is also proved that there is a dense set in E such that the critical orbit of the corresponding map enter the reversed fixed point.

Key words: unimodal map, quadratic family, invariant measure

中图分类号:

O174.12

曹永罗;王兰宇. ABUNDANCE OF UNIMODAL MAPS WITH DENSE CRITICAL ORBIT AND PREFIXED CRITICAL ORBIT[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(4): 389-394.

Cao Yongluo;Wang Lanyu. ABUNDANCE OF UNIMODAL MAPS WITH DENSE CRITICAL ORBIT AND PREFIXED CRITICAL ORBIT[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(4): 389-394.

ABUNDANCE OF UNIMODAL MAPS WITH DENSE CRITICAL ORBIT AND PREFIXED CRITICAL ORBIT

ABUNDANCE OF UNIMODAL MAPS WITH DENSE CRITICAL ORBIT AND PREFIXED CRITICAL ORBIT

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