Analytical methods in numerical ODEs
The development of new topological and algebraic tools related to the non-linear spectral theory and generalization of complex structures in commutative non-associative algebras for solution to polynomial ODEs is proposed.
The obtained methods will be used to study qualitative behavior of homogeneous polynomial systems (including the existence of bounded/periodic solutions, existence of an algebraic first integrals, etc.).
The results may be applied to studying classical quadratic systems arising in chemistry, solid body physics and engineering.