A one‐dimensional map with an infinite measure is investigated. The motions generated by the map are very sticky around indifferent fixed points. Here we report three theoretical results: First, the residence time distribution around the points is the log‐Weibull one which is same as a universal law in Hamiltonian systems. Secondly, the Darling‐Kac‐Aaronson theorem can be applied with the order α = 0. Finally, the power spectrum density of the orbits reveals the strongest non‐stationarity such as f−2 spectral fluctuations.

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