A characterization of the kneading pair for bimodal degree one circle maps
Alsedà, Lluis ; Falcó, Antonio
Annales de l'Institut Fourier, Tome 47 (1997), p. 273-304 / Harvested from Numdam
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La théorie des itinéraires symboliques développée par Milnor et Thurston donne, pour les applications de l’intervalle dans lui-même avec un nombre fini de morceaux monotones, une caractérisation de la dynamique de ces applications. Dans cet article nous apportons une caractérisation de toutes les “paires de pétrissage” pour l’ensemble des relèvements des applications continues du cercle dans lui-même de degré un bimodales.

For continuous maps on the interval with finitely many monotonicity intervals, the kneading theory developed by Milnor and Thurston gives a symbolic description of the dynamics of a given map. This description is given in terms of the kneading invariants which essentially consists in the symbolic orbits of the turning points of the map under consideration. Moreover, this theory also describes a classification of all such maps through theses invariants. For continuous bimodal degree one circle maps, similar invariants were introduced by Alsedà and Mañosas, where the first part of the program just described was carried through, and where relations between the circle maps invariants and the rotation interval were elucidated. The main theorem of this paper characterizes the set of kneading invariants for all bimodal degree one circle maps.

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     author = {Alsed\`a, Lluis and Falc\'o, Antonio},
     title = {A characterization of the kneading pair for bimodal degree one circle maps},
     journal = {Annales de l'Institut Fourier},
     volume = {47},
     year = {1997},
     pages = {273-304},
     doi = {10.5802/aif.1567},
     mrnumber = {98h:58055},
     zbl = {0861.58014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1997__47_1_273_0}
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Alsedà, Lluis; Falcó, Antonio. A characterization of the kneading pair for bimodal degree one circle maps. Annales de l'Institut Fourier, Tome 47 (1997) pp. 273-304. doi : 10.5802/aif.1567. http://gdmltest.u-ga.fr/item/AIF_1997__47_1_273_0/

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