Remarks on the characterization of periods of alternated systems

Abstract

In this note we correct a mistake inside the paper “Periodic structure of alternating continuous interval maps” (J. Differ. Equ. Appl. 12 (2006), pp. 847–858), concerning the characterization of periodic points having an odd order m greater than 1 for the alternated system $[f_1,f_2]$, and then we establish a correct formulation for the combinatorial characterization of its even periods 2m. Moreover we give a new combinatorial characterization of the periods of order m of an alternated system $[f_1,f_2,\cdots ,f_p]$ with p and m coprime.

Keywords:

• Interval maps
• alternated system
• periodic point
• shared periodic points
• periodic structure

AMS Subject Classifications:

• 37E05
• 39A11

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This paper has been supported by the [grant number MTM2011-23221] and [grant number MTM2014-52920_p] from Ministerio de Economía y Competitividad (Spain) and 19294/PI/14 from Fundación Séneca (CARM).