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Entropie et itinéraires des applications unimodales de l’intervalle. (French) Zbl 0536.54011

The partition \(\{\) [-1,0),\(\{\) 0\(\}\),(0,1]\(\}\) of \(J=[-1,1]\) defines a symbol sequence \(I_ f(x)\) for every \(x\in J\) and every unimodal map f:\(J\to J\). Following Milnor and Thurston the authors define certain sequences to be maximal itineraries and they study the topological entropy of a unimodal map f using a representation by its maximal itinerary. Other proofs of results of Jonker, Rand, Milnor and Thurston are given. [L. Jonker and D. Rand; Invent. Math. 62, 347-365 (1980; Zbl 0475.58014); ibid. 63, 1-15 (1981; Zbl 0475.58015); J. Lond. Math. Soc., II. Ser. 22, 175-181 (1980; Zbl 0437.58017)].
Reviewer: M.Denker

MSC:

54C70 Entropy in general topology
54H20 Topological dynamics (MSC2010)
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References:

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