%0 Journal Article %T A converse result concerning the periodic structure of commuting affine circle maps %A Peña, José Salvador Cánovas %A Bas, Antonio Linero %A López, Gabriel Soler %J Journal of Nonlinear Sciences and Applications %D 2016 %V 9 %N 7 %@ ISSN 2008-1901 %F Peña2016 %X 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. %9 journal article %R 10.22436/jnsa.009.07.08 %U http://dx.doi.org/10.22436/jnsa.009.07.08 %P 5041--5060