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

Annales de l'institut Fourier (1997)

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

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topAlsedà, 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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