A characterization of the kneading pair for bimodal degree one circle maps

Lluis Alsedà; Antonio Falcó

Annales de l'institut Fourier (1997)

  • Volume: 47, Issue: 1, page 273-304
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Alsedà, Lluis, and Falcó, Antonio. "A characterization of the kneading pair for bimodal degree one circle maps." Annales de l'institut Fourier 47.1 (1997): 273-304. <http://eudml.org/doc/75229>.

@article{Alsedà1997,
abstract = {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.},
author = {Alsedà, Lluis, Falcó, Antonio},
journal = {Annales de l'institut Fourier},
keywords = {circle maps; kneading invariants; rotation interval},
language = {eng},
number = {1},
pages = {273-304},
publisher = {Association des Annales de l'Institut Fourier},
title = {A characterization of the kneading pair for bimodal degree one circle maps},
url = {http://eudml.org/doc/75229},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Alsedà, Lluis
AU - Falcó, Antonio
TI - A characterization of the kneading pair for bimodal degree one circle maps
JO - Annales de l'institut Fourier
PY - 1997
PB - Association des Annales de l'Institut Fourier
VL - 47
IS - 1
SP - 273
EP - 304
AB - 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.
LA - eng
KW - circle maps; kneading invariants; rotation interval
UR - http://eudml.org/doc/75229
ER -

References

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