Periodic orbits and their bifurcations in 3-D maps with separate third iterate

Anna Agliari, Daniéle Fournier-Prunaret, Abdel Kaddous Taha

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)


We consider a class of three-dimensional maps T having the property that their third iterate has separate components. We show that the cycles of T can be obtained by those of a one-dimensional map (one of the components of T 3) and we give a complete classification of such cycles. The local bifurcations of the cycles of T are studied as well, showing that they are of co-dimension 3, since at the bifurcation value three eigenvalues simultaneously cross the unit circle. To illustrate the obtained results we consider as an example a delayed logistic map.
Original languageEnglish
Title of host publicationGlobal Analysis of Dynamic Models in Economics and Finance. Essays in Honour of Laura Gardini
EditorsG.I. Bischi, C. Chiarella, I. Sushko
Number of pages31
Publication statusPublished - 2012


  • 3D maps
  • Delayed logistic map
  • Local bifurcations
  • Multistability


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