Abstract
A continuous map f from a compact interval I into itself is densely (resp. generically) chaotic if the set of points (x, y) such that and is dense (resp. residual) in I × I. We prove that if the interval map f is densely but not generically chaotic then there is a descending sequence of invariant intervals, each of which contains a horseshoe for f2. It implies that every densely chaotic interval map is of type at most 6 for Sharkovskii's order (i.e. there exists a periodic point of period 6), and its topological entropy is at least (log 2)/2. We show that equalities can be obtained.
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