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

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.

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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