Multi-pole extension for elliptic models of interacting integrable tops: relativistic and non-relativistic cases.

We review and give detailed description for gl(NM) Gaudin models related to holomorphic vector bundles of rank NM and degree N over elliptic curve with n punctures. We present full classification for this type of integrable systems by summarizing the previously obtained results and describe the most general gl(NM) classical elliptic finite-dimensional integrable system, which includes all the known as particular cases. We also discuss relativistic analogue of these systems. We present a classification for relativistic Gaudin models on GL-bundles over elliptic curve and describe the most general gl(NM) classical elliptic finite-dimensional integrable system. Also, we provide R-matrix description for both relativistic and non-relativistic most general models through R-matrices satisfying associative Yang-Baxter equation.