Computing odd periods of alternating systems of affine circle maps

ABSTRACT

Let f,g be affine circle maps and $[f,g]$ be the alternating system generated by f and g. We present an algorithm to compute the periodic structure of $[f,g]$. This study complements the papers [J.S. Cánovas Peña, A. Linero Bas, and G. Soler López, Periods of alternated systems generated by affine circle maps, J. Difference Equ. Appl. 22 (2016), pp. 441–467; J.S. Cánovas Peña, A. Linero Bas, and G. Soler López, A converse result concerning the periodic structure of commuting affine circle maps, J. Nonlinear Sci. Appl. 9 (2016), pp. 5041–506].

KEYWORDS:

• Circle maps
• alternating system
• affine map
• periodic structure
• algorithm

MATHEMATICS SUBJECT CLASSIFICATION (2010):

• 37E10
• 37E05
• 37B55
• 11A07

Acknowledgments

We acknowledge the referees for their suggestions which allowed us to improve the reading of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Agencia Estatal de Investigación (AEI) y Fondo Europeo de Desarrollo Regional (AEI/FEDER), UE [MTM2017-84079-P] and Ministerio de Economía y Competitividad, Spain [MTM2014- 52920-P].