Electron. J. Differential Equations, Vol. 2017 (2017), No. 248, pp. 1-9.

Remarks on second-order quadratic systems in algebras

Art Sagle, Klaus Schmitt

This paper is an addendum to our earlier paper [8], where a systematic study of quadratic systems of second order ordinary differential equations defined in commutative algebras was presented. Here we concentrate on special solutions and energy considerations of some quadratic systems defined in algebras which need not be commutative, however, we shall throughout assume the algebra to be associative. We here also give a positive answer to an open question, concerning periodic motions of such systems, posed in our earlier paper.

Submitted April 14, 2017. Published October 6, 2017.
Math Subject Classifications: 34B45, 34J60, 34J65.
Key Words: Quadratic systems; ordinary differential equations; algebras; derivations; periodic motions.

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Art Sagle
Department of Mathematics
University of Hawaii-Hilo
Hilo, HI 96720, USA
email: asagle@msn.com
Klaus Schmitt
Department of Mathematics
University of Utah
155 South 1400 East
Salt Lake City, UT 84112, USA
email: schmitt@math.utah.edu

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