一类数字映射的全局结构

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The Global Bifurcation Structure of a Kind of Digit Mapping

摘要: 本文讨论映射T_n:x→[x²]_n的全局结构.T₂具有对称的不连通子结构的性质和[1]用计算机得到的结果一致.但当n=3时,这些子结构不再具有对称性了.本文得到随n增大时T_n的全局分叉结构,并得到了映射T_n,μ:x→[μx²]_n的类似结果.
- 数字映射 /
- 分叉 /
- 全局结构
Abstract: The global structure of the mapping T_n:x→[x²]_n is studied. The symmetric unconnected substructures of T₂ is coincident with [1] by computer, but for n=3 the symmetry of these substructures vanishes. As n is increasing, the global bifurcation structure of T₂ is shown. Finally, similar results for the mapping T_n:x→[μx²]_n are also proved.
- digit mapping /
- bifurcation /
- global construction

[1]	Dewdney,A.K.,Computer recreations,Scientific American,253,2(1985).16-21.
[2]	Hao Bai-lin,Elementary Symbolic Dynamics and Chaos in Dissipative System,World Scientific,Singapore(1989).
[3]	Collet,P.and J.P.Eckman,Iterated Maps on the Intervalas Dynamical System.Birkhausre,Boston(1980).