Original scientific paper

On stability of critical points of quadratic differential equations in nonassociative algebras

Borut Zalar
Matej Mencinger

Abstract

In this note we treat the stability of nonzero critical points of the differential equation x' = x2 in a commutative real nonassociative algebra. As our first result we prove that if a critical point lies in some Peirce subspace with respect to a nonzero idempotent, it cannot be stable. This improves a previously known result due to Kinyon and Sagle. As a second result we show that there exists 2-dimensional algebra

Keywords

Quadratic differential equation; nonassociative algebra; critical points; ray solutions; projections; nilpotents; Peirce subspaces

Hrčak ID:

1332

URI

https://hrcak.srce.hr/1332

Publication date:

1.6.2003.

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