Shadow lemma on the product of Hadamard manifolds and applications

In the article under review the authors study (not necessarily discrete) subgroups $\Gamma$ of the isometry group Is$(X)$ of a product $X$ of Hadamard manifolds $X_1,X_2$ with pinched negative curvature. They are particularly interested in the structure of the limit set, i.e. the set of accumulation points of the $\Gamma$-orbit of a point intersected with the ray boundary $\partial X$ of the space $X$.