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  • On stability of critical points of Riccati differential equations in nonassociative algebras
    Zalar, Borut ; Mencinger, Matej
    In this note we treat the stability of nonzero critical points of differential equation ▫$\dot{x} = x^2$▫ in a commutative real nonassociative algebra. As our first result we prove that if critical ... point lies in some Pierce subspace with respect to a nonzero idempotent, it cannot be stable. This improves previously known results due to Kinyon and Sagle. As a second result we show that there exists a 2-dimensional algebra, with nonzero critical point and nontrivial idempotent, such that the critical point is stable, so that the additional assumption in our first result cannot be completely lifted.
    Vir: Preprint series. - ISSN 1318-4865 (Vol. 39, [št.] 755, 2001, str. 1-7)
    Vrsta gradiva - članek, sestavni del
    Leto - 2001
    Jezik - angleški
    COBISS.SI-ID - 10701913

vir: Preprint series. - ISSN 1318-4865 (Vol. 39, [št.] 755, 2001, str. 1-7)

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