[2.13] Can computers simulate chaos? Strictly speaking, chaos cannot occur on computers because they deal with fi nite sets of numbers. Thus the initial condition is always precisely known, and computer experiments are perfectly predictable, in principle. In particu lar because of the finite size, every trajectory computed will eventually ha ve to repeat (an thus be eventually periodic). On the other hand, computers can effectively simulate chaotic behavior for quite long times (just so long as the discreteness is not noticeable). In particular if one uses floating point numbers in double precision to iterate a map on the unit square, then there are about 10^28 different points in the phase space, and one would exp ect the "typical" chaotic orbit to have a period of about 10^14 (this square root of the number of points estimate is given by Rannou for random diffeom orphisms and does not really apply to floating point operations, but nonethe less the period should be a big number). See, e.g., Earn, D. J. D. and S. Tremaine, "Exact Numerical Studies of Hamiltonian Maps : Iterating without Roundoff Error," Physica D 56, 1-22 (1992). Binder, P. M. and R. V. Jensen, "Simulating Chaotic Behavior with Finite Sta te Machines," Phys. Rev. 34A, 4460-3 (1986). Rannou, F., "Numerical Study of Discrete Plane Area-Preserving Mappings," As tron. and Astrophys. 31, 289-301 (1974). -- 在细雨的午後 书页里悉哩哩地传来 " 周期3 = ? " 然而我知道 当我正在日耳曼深处的黑森林 继续发掘海森堡未曾做过的梦时 康德的诺言早已远离......... 远来的传教士静静地看着山涧不断反覆叠代自己的 过去 现在 和 未来 於是仅以 一颗量子浑沌 一本符号动力学 祝那发生在周一下午的新生 --

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