When Chaos Meets Computers

by Shujun Li arXiv.org E-print Archive, 12 Dec 2005 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." Read more