The global bifurcation structure of a kind of digit mapping
Tóm tắt
The global structure of the mapping Tn:x→[x
2]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 Tn is shown. Finally, similar results for the mapping Tn, μ:x→[μx
2]n are also proved..
Tài liệu tham khảo
Dewdney, A. K., Computer recreations,Scientific American,253, 2 (1985), 16–21.
Hao Bai-lin,Elementary Symbolic Dynamics and Chaos in Dissipative System, World Scientific, Singapore (1989).
Collet, P. and J. P. Eckman,Iterated Maps on the Interval as Dynamical System, Birkhausre, Boston (1980).