Computation in One-Dimensional Piecewise Maps and Planar Pseudo-Billiard Systems
Computation in One-Dimensional Piecewise Maps and Planar Pseudo-Billiard Systems
复制标题
一维分段映射和平面伪台球系统中的计算
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
I. Potapov
中科院分区：
文献类型：
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作者：
O. Kurganskyy;I. Potapov
低维系统的计算涉及到许多长期悬而未决的问题。本文证明了由初等函数定义的一维迭代映射的普适性。迭代映射中的计算与其他非传统的计算模型有许多联系。特别地，一维迭代映射可以由平面伪台球系统来模拟。作为主要结果的结果，我们证明了平面伪台球系统不仅具有混沌行为，而且具有普适计算能力。
The computation in low-dimensional system is related to many long standing open problems. In this paper we show the universality of a one-dimensional iterative map defined by elementary functions. The computation in iterative maps have a number of connections with other unconventional models of computations. In particular, one-dimensional iterative maps can be simulated by a planar pseudo-billiard system. As a consequence of our main result we show that a planar pseudo-billiard system is not only can demonstrate a chaotic behaviour, but also has ability of universal computation.