Abstract
Any continuous interval map of type greater than 2∞ is shown to have what we call a full cascade of simple periodic orbits. This is used to prove that, for maps of any types, the existence of such a full cascade is equivalent to the existence of an infinite ω-limit set. For maps of type 2∞, this is equivalent to the existence of a (period doubling) solenoid. Hence, any map of type 2∞ which is either piecewise monotone (with finite number of pieces) or continuously differentiable has both a full cascade of simple periodic orbits and a solenoid.
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López, V.J., Snoha, L. Full cascades of simple periodic orbits on the interval. Ukr Math J 48, 1843–1851 (1996). https://doi.org/10.1007/BF02375371
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DOI: https://doi.org/10.1007/BF02375371