Suppose that you have $2D$ discrete dynamical systesm $$ \left\{\begin{array}{rcl} {\displaystyle x_{t + 1}} & {\displaystyle =} & {\displaystyle\operatorname{f}\left(x_{t},y_{t}\right)} \\ {\displaystyle y_{t + 1}} & {\displaystyle =} & {\displaystyle\operatorname{g}\left(x_t,y_t\right)} \end{array}\right. $$ and $\operatorname{f}, \operatorname{g}$ are non-linear function.
At a fixed point $\left(x^{*}, y^{*}\right)$, its linearized system is defined as follows. \begin{align} \left(x_{t + 1} - x^{*}\right) = \left[\begin{array}{cc} \frac{\partial\operatorname{f}}{\partial x} & \frac{\partial\operatorname{f}}{\partial y} \\ \frac{\partial\operatorname{g}}{\partial x} & \frac{\partial\operatorname{g}}{\partial y}\\ \end{array} \right]\left(x_{t} - x^{*}\right) \end{align} A fixed point is called center if the Jacobian matrix at a fixed point have the complex conjugate eigenvalues, and a center fixed point is called resonant if the eigenvalues are roots of unity.
I know at a resonant center fixed point, the linearized system have periodic orbits near the origin, but what is the result of being resonant on the former non-linear system ( I can't have the image of the concept "resonance" )\ $?$.