Abstract
It was proved that all continuous functions are topologically conjugate to their continuous iterative roots in monotonic cases. An interesting problem reads: Does the same conclusion hold in non-monotonic cases? We give a negative answer to the problem by presenting a necessary condition for the topological conjugacy, which helps us construct counter examples. We also give a sufficient condition as well as a method of constructing the topological conjugacy.
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Li, L., Zhang, W. Conjugacy between piecewise monotonic functions and their iterative roots. Sci. China Math. 59, 367–378 (2016). https://doi.org/10.1007/s11425-015-5065-6
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DOI: https://doi.org/10.1007/s11425-015-5065-6