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Universal Form of Renormalizable Knots in Symbolic Dynamics of Bimodal Maps
Wen Gao 1,Chuan-Yun Xu 2,Shou-Li Peng 2,Ke-Fei Cao 2 *
1.School of Statistics and Mathematics, Yunnan University of Finance and Economics
2.Center for Nonlinear Complex Systems, Department of Physics, Yunnan University
*Correspondence author
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Funding: 国家自然科学基金,教育部博士点基金,云南大学理（工）科校级科研项目（No.10565004,20050673001,2005Q018C）
Opened online:22 January 2009
Accepted by: none
Citation: Wen Gao,Chuan-Yun Xu,Shou-Li Peng.Universal Form of Renormalizable Knots in Symbolic Dynamics of Bimodal Maps[OL]. [22 January 2009] http://en.paper.edu.cn/en_releasepaper/content/28262
 
 
The universal relation between knot theory and symbolic dynamics is established in bimodal maps in this paper. When symbolic sequences of maps are expressed as simple knots, it is easy to find that knots for renormalizable sequences are constructed of bunches of flows. They are parallel, inverse parallel or single-folding. The generation of renormalizable knots can be operated easily in geometry or be calculated by algebraic method. Especially, it is independent of traditional star product of symbolic dynamics. We present some examples and list them in a table with period not beyond 6.
Keywords:Symbolic dynamics;Knot;Renormalization;Bimodal maps
 
 
 

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