On orbital topological equivalence of cubic ODEs in two-dimensional algebras

Zolman Balanov, Wiesław Krawcewicz, Shira Zur

DOI: http://dx.doi.org/10.12775/TMNA.2005.011

Abstract


Cubic 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.

Keywords


Non-associative algebras; polynomial equations in algebra; complex structures; quadratic and cubic differential systems in algebras; bounded solutions; orbital topological equivalence of phase portraits.

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