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A two-dimensional mapping with a strange attractor. (English) Zbl 0576.58018
The author considers the iteration x i+1 =y i +1-ax i 2 , y i+1 =bx i , x i ,y i ,a,bR, and shows that there are points (x 0 ,y 0 ) such that the corresponding {(x n ,y n )} sequences tend to a ”strange attractor”.

MSC:
37D45Strange attractors, chaotic dynamics
References:
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[3]Engel, W.: Math. Annalen136, 319 (1958) · Zbl 0082.36502 · doi:10.1007/BF01360237
[4]Hénon, M.: Quart. Appl. Math.27, 291 (1969)
[5]Lanford, O.: Work cited by Ruelle, 1975
[6]Lorenz, E. N.: J. atmos. Sci.20, 130 (1963) · doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
[7]Pomeau, Y.: to appear (1976)
[8]Ruelle, D., Takens, F.: Comm. math. Phys.20, 167;23, 343 (1971)
[9]Ruelle, D.: Report at the Conference on ”Quantum Dynamics Models and Mathematics” in Bielefeld, September 1975