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The dyadic transformation (also known as the dyadic map, bit shift map, 2''x'' mod 1 map, Bernoulli map, doubling map or sawtooth map〔(Chaotic 1D maps ), Evgeny Demidov〕〔Wolf, A. "Quantifying Chaos with Lyapunov exponents," in ''Chaos'', edited by A. V. Holden, Princeton University Press, 1986.〕) is the mapping (i.e., recurrence relation) : : produced by the rule : : .〔[http://www.maths.bristol.ac.uk/~maxcu/Doubling.pdf Dynamical Systems and Ergodic Theory - The Doubling Map], Corinna Ulcigrai, University of Bristol〕 Equivalently, the dyadic transformation can also be defined as the iterated function map of the piecewise linear function : The name ''bit shift map'' arises because, if the value of an iterate is written in binary notation, the next iterate is obtained by shifting the binary point one bit to the right, and if the bit to the left of the new binary point is a "one", replacing it with a zero. The dyadic transformation provides an example of how a simple 1-dimensional map can give rise to chaos. ==Relation to tent map and logistic map== The dyadic transformation is topologically conjugate to : * the unit-height tent map * the chaotic ''r'' = 4 case of the logistic map. The ''r'' = 4 case of the logistic map is ; this is related to the bit shift map in variable ''x'' by : There is semi-conjugacy between the dyadic transformation (here named angle doubling map) and the quadratic polynomial. Here map doubles angles measured in turns. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「dyadic transformation」の詳細全文を読む スポンサード リンク
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