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

37D45Strange attractors, chaotic dynamics
Full Text: DOI
[1] Birkhoff, G. D.: Trans. Amer. Math. Soc.18, 199 (1917) · doi:10.1090/S0002-9947-1917-1501070-3
[2] Engel, W.: Math. Annalen130, 11 (1955) · Zbl 0065.02603 · doi:10.1007/BF01343190
[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) · Zbl 0227.76084
[9] Ruelle, D.: Report at the Conference on ”Quantum Dynamics Models and Mathematics” in Bielefeld, September 1975