Dynamical systems of an infinite-dimensional non-linear operator

This talk is devoted to fixed points of an infinite-dimensional operator $F$ mapping $l_{+}^{1}$ to itself. We show that this operator may have up to seven fixed points. We illustrate that analyzing our operator can be simplified to a two-dimensional approach. We provide a detailed description of all fixed points for the two-dimensional operator and determine the set of limit points for its trajectories. Finally, we apply these results to determine the set of limit points for trajectories generated by the infinite-dimensional operator.