When Chaos Meets Computers

Details When Chaos Meets Computers When Chaos Meets Computers

2004-05-14

arxiv.org/abs/nlin/0405038v3

Nonlinear Sciences

Chaotic Dynamics

7 pages, 5 figures

Scientific paper

This paper focuses on an interesting phenomenon when chaos meets computers. It is found that digital computers are absolutely incapable of showing true long-time dynamics of some chaotic systems, including the tent map, the Bernoulli shift map and their analogues, even in a high-precision floating-point arithmetic. Although the results cannot directly generalized to most chaotic systems, the risk of using digital computers to numerically study continuous dynamical systems is shown clearly. As a result, we reach the old saying that "it is impossible to do everything with computers only".

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