Glasnik matematički, Vol. 38 No. 1, 2003.
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
Publication date:
1.6.2003.
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