Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (5): 671-682.doi: https://doi.org/10.1007/s10483-016-2080-9

• 论文 • 上一篇    

Symbolic dynamics of Belykh-type maps

Denghui LI, Jianhua XIE   

  1. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China
  • 收稿日期:2015-06-06 修回日期:2015-09-20 出版日期:2016-05-01 发布日期:2016-05-01
  • 通讯作者: Jianhua XIE E-mail:jhxie2000@126.com
  • 基金资助:

    Project supported by the National Natural Science Foundation of China (Nos. 11172246 and 11572263)

Symbolic dynamics of Belykh-type maps

Denghui LI, Jianhua XIE   

  1. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China
  • Received:2015-06-06 Revised:2015-09-20 Online:2016-05-01 Published:2016-05-01
  • Contact: Jianhua XIE E-mail:jhxie2000@126.com
  • Supported by:

    Project supported by the National Natural Science Foundation of China (Nos. 11172246 and 11572263)

摘要:

The symbolic dynamics of a Belykh-type map (a two-dimensional discontinuous piecewise linear map) is investigated. The admissibility condition for symbol sequences named the pruning front conjecture is proved under a hyperbolicity condition. Using this result, a symbolic dynamics model of the map is constructed according to its pruning front and primary pruned region. Moreover, the boundary of the parameter region in which the map is chaotic of a horseshoe type is given.

关键词: symbolic dynamics, pruning front, discontinuous piecewise linear map, primary pruned region, horseshoe

Abstract:

The symbolic dynamics of a Belykh-type map (a two-dimensional discontinuous piecewise linear map) is investigated. The admissibility condition for symbol sequences named the pruning front conjecture is proved under a hyperbolicity condition. Using this result, a symbolic dynamics model of the map is constructed according to its pruning front and primary pruned region. Moreover, the boundary of the parameter region in which the map is chaotic of a horseshoe type is given.

Key words: symbolic dynamics, pruning front, discontinuous piecewise linear map, primary pruned region, horseshoe

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