Cánovas, Jose S.; Linero, Antonio Periodic structure of alternating continuous interval maps. (English) Zbl 1099.37028 J. Difference Equ. Appl. 12, No. 8, 847-858 (2006). Summary: Given two continuous interval maps \(f\) and \(g\), we study the periodic structure for the set of sequences \((x_n)\in[0,1]^\mathbb{N}\) generated by \(f\) and \(g\) by the rule \((x_1,f(x_1),g(f(x_1)), f(g(f(x_1)))\), \(\dots)\). It is shown that this structure is intimately related to that of Sharkovsky’s theorem, although some differences appear with the periods that are coprime with 2. Cited in 2 ReviewsCited in 18 Documents MSC: 37E05 Dynamical systems involving maps of the interval (piecewise continuous, continuous, smooth) 37B20 Notions of recurrence and recurrent behavior in dynamical systems 37E99 Low-dimensional dynamical systems Keywords:discrete dynamical system; set of periods; Sharkovsky’s theorem; continuous interval maps; forcings PDF BibTeX XML Cite \textit{J. S. Cánovas} and \textit{A. Linero}, J. Difference Equ. Appl. 12, No. 8, 847--858 (2006; Zbl 1099.37028) Full Text: DOI References: [1] DOI: 10.1063/1.1397769 · Zbl 0977.37049 · doi:10.1063/1.1397769 [2] DOI: 10.1016/j.jmaa.2005.04.059 · Zbl 1125.39001 · doi:10.1016/j.jmaa.2005.04.059 [3] Alsedà L., Combinatorial Dynamics and Entropy in Dimension One (1993) · Zbl 0843.58034 · doi:10.1142/1980 [4] DOI: 10.1007/PL00000152 · Zbl 0991.37016 · doi:10.1007/PL00000152 [5] DOI: 10.1080/1023619021000047789 · Zbl 1030.39005 · doi:10.1080/1023619021000047789 [6] DOI: 10.1103/PhysRevE.69.021906 · doi:10.1103/PhysRevE.69.021906 [7] DOI: 10.3934/dcds.2000.6.893 · Zbl 1011.37023 · doi:10.3934/dcds.2000.6.893 [8] Dinis L., Physics A 343 pp 701– (2004) · doi:10.1016/j.physa.2004.06.076 [9] DOI: 10.2307/4145161 · Zbl 1187.37054 · doi:10.2307/4145161 [10] DOI: 10.1016/j.jde.2003.10.024 · Zbl 1067.39003 · doi:10.1016/j.jde.2003.10.024 [11] DOI: 10.1080/00107510310001644836 · doi:10.1080/00107510310001644836 [12] DOI: 10.1103/PhysRevLett.85.5226 · doi:10.1103/PhysRevLett.85.5226 [13] Sharkovsky A.N., Ukrain. Mat. Zh. 16 pp 61– (1964) [14] DOI: 10.1207/s15427579jpfm0601_3 · doi:10.1207/s15427579jpfm0601_3 [15] DOI: 10.1142/S0219477502000907 · doi:10.1142/S0219477502000907 [16] DOI: 10.1016/j.physa.2004.11.024 · doi:10.1016/j.physa.2004.11.024 [17] DOI: 10.1016/j.jtbi.2004.11.020 · doi:10.1016/j.jtbi.2004.11.020 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.