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Periodic structure of alternating continuous interval maps. (English) Zbl 1099.37028
Summary: Given two continuous interval maps \(f\) and \(g\), we study the periodic structure for the set of sequences \((x_n)\in[0,1]^\mathbb{N}\) generated by \(f\) and \(g\) by the rule \((x_1,f(x_1),g(f(x_1)), f(g(f(x_1)))\), \(\dots)\). It is shown that this structure is intimately related to that of Sharkovsky’s theorem, although some differences appear with the periods that are coprime with 2.

MSC:
37E05 Dynamical systems involving maps of the interval (piecewise continuous, continuous, smooth)
37B20 Notions of recurrence and recurrent behavior in dynamical systems
37E99 Low-dimensional dynamical systems
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