On orbital topological equivalence of cubic ODEs in two-dimensional algebras
KeywordsNon-associative algebras, polynomial equations in algebra, complex structures, quadratic and cubic differential systems in algebras, bounded solutions, orbital topological equivalence of phase portraits.
AbstractCubic differential systems in real commutative two-dimensional algebras are classified up to orbital topological equivalence via the solubility of polynomial equations in algebras. As a by-product, existence of bounded solutions in such systems is studied via complex structures in the algebras. Application to the existence of periodic solutions to $n$-dimensional differential systems "cubic at infinity" is given.
How to Cite
BALANOV, Zolman, KRAWCEWICZ, Wiesław & ZUR, Shira. On orbital topological equivalence of cubic ODEs in two-dimensional algebras. Topological Methods in Nonlinear Analysis [online]. 1 June 2005, T. 25, nr 2, s. 205–234. [accessed 25.3.2023].
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