Abstract
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.
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Kurganskyy, O., Potapov, I. (2005). Computation in One-Dimensional Piecewise Maps and Planar Pseudo-Billiard Systems. In: Calude, C.S., Dinneen, M.J., Păun, G., Pérez-Jímenez, M.J., Rozenberg, G. (eds) Unconventional Computation. UC 2005. Lecture Notes in Computer Science, vol 3699. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11560319_16
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DOI: https://doi.org/10.1007/11560319_16
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