Geodesic
A converse result concerning the periodic structure of commuting affine circle maps
Peña, José Salvador Cánovas1 ; Bas, Antonio Linero2 ; López, Gabriel Soler3
1 Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Campus Muralla del Mar, 30203{Cartagena, Spain
2 Department of Mathematics, Universidad de Murcia, Campus de Espinardo, 30100-Murcia, Spain
3 Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Alfonso XIII 52, 30203{Cartagena, Spain
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 7, p. 5041-5060.

Voir la notice de l'article provenant de la source International Scientific Research Publications

We analyze the set of periods of a class of maps $\phi_{d,\kappa}: \mathbb{Z}_\Delta\rightarrow \mathbb{Z}_\Delta$ defined by $\phi_{d,\kappa}(x)=dx+\kappa,\quad d,\kappa\in\mathbb{Z}_\Delta$, where $\Delta$ is an integer greater than 1. This study is important to characterize completely the period sets of alternated systems $f; g; f; g,... $, where $f; g : \mathbb{S}_1 \rightarrow \mathbb{S}_1$ are affine circle maps that commute, and to solve the converse problem of constructing commuting affine circle maps having a prescribed set of periods.
DOI : 10.22436/jnsa.009.07.08
Classification : 37E10, 11A07
Keywords: Affine maps, alternated system, periods, circle maps, degree, combinatorial dynamics, ring of residues modulo m, Abelian multiplicative group of residues modulo m, Euler function, congruence, order, generator.

Peña, José Salvador Cánovas 1 ; Bas, Antonio Linero 2 ; López, Gabriel Soler 3

1 Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Campus Muralla del Mar, 30203{Cartagena, Spain
2 Department of Mathematics, Universidad de Murcia, Campus de Espinardo, 30100-Murcia, Spain
3 Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Alfonso XIII 52, 30203{Cartagena, Spain 
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Peña, José Salvador Cánovas; Bas, Antonio Linero; López, Gabriel Soler. A converse result concerning the periodic structure of commuting affine circle maps. Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 7, p. 5041-5060. doi : 10.22436/jnsa.009.07.08. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.07.08/

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