The Global Bifurcation Structure of a Kind of Digit Mapping

Lu Qin-he; Xu Zheng-fan; Lin Fu-qin; Liu Zeng-rong

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Article Navigation > Applied Mathematics and Mechanics > 1991 > 12(2): 185-193

Lu Qin-he, Xu Zheng-fan, Lin Fu-qin, Liu Zeng-rong. The Global Bifurcation Structure of a Kind of Digit Mapping[J]. Applied Mathematics and Mechanics, 1991, 12(2): 185-193.

Citation:

Lu Qin-he, Xu Zheng-fan, Lin Fu-qin, Liu Zeng-rong. The Global Bifurcation Structure of a Kind of Digit Mapping[J]. Applied Mathematics and Mechanics, 1991, 12(2): 185-193.

Citation:

Lu Qin-he, Xu Zheng-fan, Lin Fu-qin, Liu Zeng-rong. The Global Bifurcation Structure of a Kind of Digit Mapping[J]. Applied Mathematics and Mechanics, 1991, 12(2): 185-193.

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The Global Bifurcation Structure of a Kind of Digit Mapping

1.
Suzhou University, Jiangsu;
2.
Shanghai Maritime University, Shanghai

Received Date: 1990-03-23
Publish Date: 1991-02-15

Abstract

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

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References(3)

References

[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).