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Entropy of n-Fold Compositions of the Tent Map

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Define a tent map by

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where , ; has a maximum at .

Let be the function composed with itself times and let be the number of intervals over which is monotone; for the tent maps considered here, is twice the number of maxima of .

Define the entropy to be .

For the tent map with maximum at , the entropy of is 1, as the number of maxima is .

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Contributed by: John Wells (November 2010)
Suggested by: Christopher Mouron
Open content licensed under CC BY-NC-SA

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