| MSC: | 39A11 | Stability and asymptotics of difference equations; oscillatory and periodic solutions, etc. |
| 41A60 |
Abstract:
For ten nonlinear difference equations with only $p$-periodic
solutions it is shown that the characteristic polynomials of the
corresponding linearized equations about the equilibria have
only zeros which are $p$-th roots of unity. An analogous result is
shown concerning two systems of such equations.
Five counterexamples show that the reverse is not true.
Some remarks are
made concerning equations with asymptotically $p$-periodic solutions.