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On cusps and flat tops

Neil Dobbs — 2014

Annales de l’institut Fourier

Non-invertible Pesin theory is developed for a class of piecewise smooth interval maps which may have unbounded derivative, but satisfy a property analogous to C 1 + ϵ . The critical points are not required to verify a non-flatness condition, so the results are applicable to C 1 + ϵ maps with flat critical points. If the critical points are too flat, then no absolutely continuous invariant probability measure can exist. This generalises a result of Benedicks and Misiurewicz.

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