TY - JOUR AU - Peña, José Salvador Cánovas AU - Bas, Antonio Linero AU - López, Gabriel Soler PY - 2016 TI - A converse result concerning the periodic structure of commuting affine circle maps JO - Journal of Nonlinear Sciences and Applications SP - 5041--5060 VL - 9 IS - 7 AB - 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. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.009.07.08 DO - 10.22436/jnsa.009.07.08 ID - Peña2016 ER - TY - BOOK TI - Combinatorial dynamics and entropy in dimension one, Advanced Series in Nonlinear Dynamics AU - L. Alsedà AU - J. Llibre AU - M. Misiurewicz PB - World Scientific Publishing Co., Inc. PY - 1993 DA - 1993// CY - River Edge, NJ ID - Alsedà1993 ER - TY - BOOK TI - Introduction to analytic number theory, Undergraduate Texts in Mathematics AU - T. M. Apostol PB - Springer-Verlag PY - 1976 DA - 1976// CY - New York-Heidelberg ID - Apostol1976 ER - TY - JOUR TI - The topology of algebra: combinatorics of squaring AU - V. I. Arnold JO - (Russian) Funktsional. Anal. i Prilozhen., 37 (2003), 20-35, translation in Funct. Anal. Appl. PY - 2003 DA - 2003// VL - 37 ID - Arnold2003 ER - TY - JOUR TI - Periodic structure of alternating continuous interval maps AU - J. S. Cánovas AU - A. Linero JO - J. Difference Equ. Appl. PY - 2006 DA - 2006// VL - 12 ID - Cánovas2006 ER - TY - JOUR TI - Periods of alternated systems generated by affine circle maps AU - J. S. Cánovas AU - A. Linero Bas AU - G. Soler López JO - J. Difference Equ. Appl. PY - 2016 DA - 2016// VL - 22 ID - Cánovas2016 ER - TY - BOOK TI - Advances in discrete dynamics (Chapter 1. Periodic structure of discrete dynamical systems and global periodicity) AU - A. Linero Bas PB - Nova Science Publishers PY - 2013 DA - 2013// CY - NY, USA ID - Bas2013 ER - TY - JOUR TI - Co-existence of cycles of a continuous mapping of the line into itself AU - O. M. Šarkovskiĭ JO - (Russian) Ukrain. Mat. Z. PY - 1964 DA - 1964// VL - 16 ID - Šarkovskiĭ1964 ER - TY - JOUR TI - n cycles and the structure of a continuous mapping AU - O. M. Šarkovskiĭ JO - (Russian) Ukrain. Mat. Z. PY - 1965 DA - 1965// VL - 17 ID - Šarkovskiĭ1965 ER - TY - JOUR TI - Coexistence of cycles of a continuous map of the line into itself, Translated from the Russian by J. Tolosa, Proceedings of the Conference ''Thirty Years after Sharkovskiĭ's Theorem: New Perspectives'' AU - A. N. Šharkovskiĭ JO - Murcia, (1994), Internat. J. Bifur. Chaos Appl. Sci. Engrg. PY - 1995 DA - 1995// VL - 5 ID - Šharkovskiĭ1995 ER - TY - JOUR TI - Topology of dynamical systems in finite groups and number theory AU - R. Uribe-Vargas JO - Bull. Sci. Math. PY - 2006 DA - 2006// VL - 130 ID - Uribe-Vargas2006 ER -