Geodesic
A note on periods of powers
J.S. Cánovas1 ; A. Linero Bas2
1 Universidad Politécnica de Cartagena, Departamento de Matemática Aplicada y Estadística, Escuela Técnca Superior de Ingenieros Industriales, 30202 Cartagena (Spain).
2 Universidad de Murcia, Departamento de Matemáticas, Campus de Espinardo, 30100 Murcia (Spain).
ESAIM. Proceedings, Tome 46 (2014), pp. 125-131.

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Let f:X → X be a continuous map defined from a topological space X into itself. We discuss the problem of analyzing and computing explicitly the set Per(fp) of periods of the p-th iterate fp from the knowledge of the set Per(f) of periods of f. In the case of interval or circle maps, that is, X = [0,1] or X = S1, this question was solved in [11]. Now, we present some remarks and advances concerning the set Per(fp) for a continuous interval map, and on the other hand we study and solve the problem when we consider σ-permutation maps, namely, when X = [0,1] k for some integer k ≥ 2 and the map has the form F(x1,x2,...,xk) = (fσ(1)(xσ(1)),fσ(2)(xσ(2)),...,fσ(k)(xσ(k))), being each fj a continuous interval map and σ a cyclic permutation of {1,2,...,k}. This paper can be seen as the continuation of [11].
DOI : 10.1051/proc/201446011

J.S. Cánovas 1 ; A. Linero Bas 2

1 Universidad Politécnica de Cartagena, Departamento de Matemática Aplicada y Estadística, Escuela Técnca Superior de Ingenieros Industriales, 30202 Cartagena (Spain).
2 Universidad de Murcia, Departamento de Matemáticas, Campus de Espinardo, 30100 Murcia (Spain). 
@article{EP_2014_46_a11,
     author = {J.S. C\'anovas and A. Linero Bas},
     title = {A note on periods of powers},
     journal = {ESAIM. Proceedings},
     pages = {125--131},
     publisher = {mathdoc},
     volume = {46},
     year = {2014},
     doi = {10.1051/proc/201446011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201446011/}
}
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J.S. Cánovas; A. Linero Bas. A note on periods of powers. ESAIM. Proceedings, Tome 46 (2014), pp. 125-131. doi : 10.1051/proc/201446011. http://geodesic.mathdoc.fr/articles/10.1051/proc/201446011/

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