A self-invertibility condition for global periodicity of difference equations. (English) Zbl 1120.39002
The author considers the global periodicity i.e. periodicity of all solutions with the same period \(p\) for the difference equation
\[
y_{n+1}=f(y_n,\ldots,y_{n-k+1}),\quad k\geq 2
\]
with the first order difference equation
\[
z_{n+1}=g(z_n)
\]
which has global periodicity of prime period 1 or 2 if and only if \(g^{-1}(x)=g(x)\). In the general case an analogous condition appears to be only necessary for the global periodicity.
Reviewer: Vladimir Răsvan (Craiova)
MSC:
| 39A11 | Stability of difference equations (MSC2000) |
| 39A12 | Discrete version of topics in analysis |
References:
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