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Stable and non-stable non-chaotic maps of the interval. (English) Zbl 0762.58014
The paper deals with piecewise monotonic functions of the interval on itself. Other than the construction of a non-chaotic non-stable map, the author shows that every piecewise monotonic non-chaotic function is stable and that for any given piecewise monotonic function with zero topological entropy, every infinite \(\omega\)-limit set is perfect.

MSC:
37E99 Low-dimensional dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37C75 Stability theory for smooth dynamical systems
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References:
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