Continued Fractions and Chaos (Organic Mathematics Proceedings)
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|Robert M. Corless|
|From the Proceedings of the Organic Mathematics Workshop. This paper is meant for the reader who knows something about continued fractions, and wishes to know more about the theory of chaotic dynamical systems; it is also useful for the person who knows something about chaotic dynamical systems but wishes to see clearly what the effects of numerical simulation of such a system are. This paper is not purely introductory, however: there are new dynamical systems results presented here and also in the companion paper, which contains some discussion of dynamical reconstruction techniques and dimension estimates. Contents include: historical background, including the Gauss map; dynamical systems terminology; classical results interpreted in dynamical systems terminology (periodic and fixed points of the Gauss map, aperiodic points, Lyapunov exponents, and ergodic results); and the floating-point Gauss map. See also http://www.cecm.sfu.ca/organics/papers/corless/.|
|Math Topics:||Dynamical Systems, Chaos, Number Theory|
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