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Continued fractions and chaos. (English) Zbl 0758.58020

It is shown that the Gauss map \(G\), \(G(x)=0\text{ if }x=0\), \(G(x)=1/x\) if \(x\neq 0\), exhibits all the common features of a chaotic discrete dynamical system. The relationship of numerical simulation of the map to the exact map is explored. The Lyapunov exponents of the Gauss map are accurately calculated from the simulation; a new method for calculating \(\pi\) is given.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
30B70 Continued fractions; complex-analytic aspects
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