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Non-existence of wandering intervals and structure of topological attractors of one dimensional dynamical systems. II: The smooth case. (English) Zbl 0665.58024
This paper is the continuation of part I [see the preceding article]. Let $${\mathcal A}$$ be the class of $$C^ 3$$-smooth one dimensional maps f: $$M\to M$$ with nondegenerate critical points. Theorem. A map $$f\in {\mathcal A}$$ has no wandering intervals.
The theorem is proved by combining the technique of part I with the distortion estimates due to W. de Melo and S. J. van Strien [ibid. 7, 415-462 (1987; Zbl 0609.58023)] (in that paper the absence of wandering intervals for unimodal $$f\in {\mathcal A}$$ was established). The main new point is the analysis of intersection multiplicity of intervals in some specific situation.
Reviewer: M.Yu.Lyubich

##### MSC:
 37C70 Attractors and repellers of smooth dynamical systems and their topological structure 37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
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##### References:
 [1] van Strien, Hyperbolicity and invariant measures for general C pp 87– [2] Lyubich, Ergod. Th. & Dyn. Sys. none pp none– (none) [3] Melo, A structure theorem in one dimensional dynamics (1986)
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