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A chaotic function whose nonwandering set is the Cantor ternary set. (English) Zbl 0592.26007

For the mapping \(f(x)=-3x+1\) for \(x\in [0,1/3]\), \(f(x)=0\) for \(x\in [1/3,2/3]\) and \(f(x)=3x-2\) for \(x\in [2/3,1]\) the author shows that the nonwandering set is the Cantor set and characterizes the periodic points and recurrent points of f using their ternary expansions.
Reviewer: J.Smítal

MSC:

26A18 Iteration of real functions in one variable
54H20 Topological dynamics (MSC2010)
37Cxx Smooth dynamical systems: general theory
Full Text: DOI

References:

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