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Typical limit sets of critical points for smooth interval maps. (English) Zbl 0958.37011

The paper deals with \(C^r\)-structurally stable maps for \(r=2\) and continues previous research of the authors in this direction. More precisely, the authors prove that for a dense set of maps the limit set of every critical point is minimal. One of the main tools the authors use are so-called chains, which were introduced by Lyubich for interval maps with negative Schwarzian.

MSC:

37E05 Dynamical systems involving maps of the interval
37C20 Generic properties, structural stability of dynamical systems
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