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On the metric properties of multimodal interval maps and \(C^2\) density of Axiom A. (English) Zbl 1057.37039

This extended work is well written and organized. It is a good example of a “reader-friendly” paper. The central part of this work is to gain control on the geometry of a multimodal interval map. The work is a natural continuation of the recent research on unimodal interval maps. The author proves that Axiom A maps are dense in the space of \(C^2\) interval maps endowed with the \(C^2\)-topology and that \(C^2\)-structurally stable maps satisfy Axiom A and form an open dense subset of \(C^2([0,1][0,1])\).

MSC:

37E05 Dynamical systems involving maps of the interval
37F25 Renormalization of holomorphic dynamical systems
37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
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