# Blaszak M. Bi-presymplectic theory of Stackel systems, talk at The Workshop on GDEq and Integrability, 11-15 October 2010, Hradec nad Moravici, Czech Republic (abstract)

Bi-presymplectic chains of one-forms of arbitrary co-rank are considered. The conditions in which such chains represent some Liouville integrable systems and the conditions in which there exist related bi-Hamiltonian chains of vector fields are presented. In order to derive the construction of bi-presymplectic chains, the notions of dual Poisson-presymplectic pair, ${\displaystyle d}$-compatibility of presymplectic forms and ${\displaystyle d}$-compatibility of Poisson bivectors is used. The completely algorithmic construction of separation coordinates is demonstrated. It is also proved that Stäckel separable systems have bi-inverse-Hamiltonian representation, i.e., are represented a by bi-presymplectic chains of closed one-forms. The co-rank of related structures depends on the explicit form of separation relations.