Étude de la classification topologique des fonctions unimodales
Cosnard, Michel
Annales de l'Institut Fourier, Tome 35 (1985), p. 59-77 / Harvested from Numdam
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À l’aide de la théorie des itinéraires et des suites de tricotage, nous étudions la conjugaison topologique des fonctions unimodales. Nous introduisons la notion de conjugaison macroscopique, caractérisée par l’égalité des suites de tricotage. Puis nous présentons un théorème de classification des fonctions unimodales. Pour illustrer ces résultats, nous montrons que l’ensemble des solutions de l’équation de Feigenbaum contient une infinité de classes topologiques.

Using the theory of itineraries and kneading sequences, we study the topological conjugacy of unimodal functions. We introduce the notion of macroscopical conjugacy, characterized by the equality of the kneading sequences. Then we present a theorem of classification of unimodal functions. In order to illustrate these results, we show that the set of solutions of Feigenbaum equation contains an infinite number of classes.

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     author = {Cosnard, Michel},
     title = {\'Etude de la classification topologique des fonctions unimodales},
     journal = {Annales de l'Institut Fourier},
     volume = {35},
     year = {1985},
     pages = {59-77},
     doi = {10.5802/aif.1019},
     mrnumber = {87i:58091},
     zbl = {0569.58004},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_1985__35_3_59_0}
}

Cosnard, Michel. Étude de la classification topologique des fonctions unimodales. Annales de l'Institut Fourier, Tome 35 (1985) pp. 59-77. doi : 10.5802/aif.1019. http://gdmltest.u-ga.fr/item/AIF_1985__35_3_59_0/

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