Date of Original Version
By using the KAM theory, we investigate the stability of the equilibrium solution of a certain difference equation. We also use the symmetries to find effectively the periodic solutions with feasible periods. The specific feature of this difference equation is the fact that we were not able to use the invariant to prove stability or to find feasible periods of the solutions.
Jašarević-Hrustić, S., Nurkanović, Z., Kulenović, M. R. S., & Pilav, E. (2015). Birkhoff Normal Forms, KAM Theory and Symmetries for Certain Second Order Rational Difference Equation with Quadratic Term. International Journal of Difference Equations, 10(2), 181-199.
Available at: http://campus.mst.edu/ijde/contents/v10n2p4.pdf