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Information × Registration Number 0206U000681, 0101U000193 , R & D reports Title Investigation of differential-geometric and topological structures associated with dynamical systems on manifolds popup.stage_title Head Prykarpatsky A. K., Registration Date 02-02-2006 Organization Pidstryhach Institute for Applied Problems of Mechanics and Mathematics NASU popup.description2 3. The undegrounds of the commutative and non-commutative theory of integrability of non-linear Hamiltonian systems on canonical simplectic manifolds are presented. The basic concepts of finite dimensional reductions of non-linear dynamical systems on functional manifolds with symmetry are stated. The de Rham-Hodge type theory for differential operator complexes in several variables is developed. An analitic solution of the Gelfand-Levitan-Marchenko integral equations for the Sturm-Liouville operator with staircase potential is founded. Some corelations between invariants of finite order and classical invariants of knots are given. The Lie-algebraic structure of integrable multivariable dynamical systems on functional manifolds is investigated. Product Description popup.authors popup.nrat_date 2020-04-02 Close