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Some results on periodicity of difference equations. (English) Zbl 1382.39018
Liz, Eduardo (ed.) et al., Proceedings of the workshop on future directions in difference equations, Vigo, Spain, June 13–17, 2011. Vigo: Servizo de Publicacións da Universidade de Vigo (ISBN 978-84-8158-541-4/pbk). Colección Congresos 69, 121-143 (2011).
Summary: We will deal with the topic of the periodicity for difference equations with real values. In the autonomous case, \(x_{n+k}=f(x_{n+k-1},\dots,x_n)\), we will survey two topics: the forcing relations of periods and the global periodicity. In the non-autonomous case, \(x_{n+k}=f(n,x_{n+k-1},\dots,x_n)\), we focus our attention on periodic non-autonomous difference equations given by \(x_{n+1}=f_{n\pmod p}(x_n)\), with \(n\geq 1\). For these equations, we present a Sharkovsky type result characterizing their periodic structure. In both the autonomous and the non-autonomous case, we pose some open problems.
For the entire collection see [Zbl 1230.00047].

MSC:
39A23 Periodic solutions of difference equations
37E15 Combinatorial dynamics (types of periodic orbits)
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