Non-autonomous 2-periodic Gumovski-Mira difference equations

Abstract

We consider two types of non-autonomous 2-periodic Gumovski-Mira difference equations. We show that while the corresponding autonomous recurrences are conjugated, the behavior of the sequences generated by the 2-periodic ones differ dramatically: in one case the behavior of the sequences is simple (integrable) and in the other case it is much more complicated (chaotic). We also present a global study of the integrable case that includes which periods appear for the recurrence.

20 pages, 11 figures

References in corpus (4)

• Studying discrete dynamical systems trough differential equations
• Dynamics of the third order Lyness' difference equation
• Integrability and non-integrability of periodic non-autonomous Lyness recurrences
• On two and three periodic Lyness difference equations

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