Abstract
We consider the dynamics in a special case of two‐dimensional quadratic homogeneous discrete dynamical systems. It is well known (c.f. [1, 2]) that homogeneous quadratic maps are in one to one correspondence with two‐dimensional commutative (nonassociative) algebras. Algebraic concepts (such as the structure of algebra and existence of special elements like idempotents and nilpotents) help us to study the dynamics of the corresponding discrete homogeneous quadratic maps. It is well‐known that such systems can exhibit chaotic behavior [3], In this article we consider the influence of the existence of an algebra ideal on the dynamics of the corresponding discrete homogeneous quadratic system. We also present some examples in the plane.
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