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Quadratic differential equations in  -graded algebras
Author(s):
Nora
C.
Hopkins;
Michael
K.
Kinyon
Journal:
Trans. Amer. Math. Soc.
351
(1999),
4545-4559.
MSC (1991):
Primary 34C35, 17A60, 34C20, 17A36
Posted:
July 19, 1999
MathSciNet review:
1475685
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Abstract:
Quadratic differential equations whose associated algebra has an automorphism of order two are studied. Under hypotheses that naturally generalize the cases where the even or odd part of the algebra is one dimensional, the following are examined: structure theory of the associated algebra (ideal structure, simplicity, solvability, and nilpotence), derivations and first integrals, trajectories given by derivations, and Floquet decompositions.
References:
- 1.
- A. Brauer and C. Noel, Qualitative Theory of Ordinary Differential Equations, Dover Press, 1970.
- 2.
- N. C. Hopkins, Quadratic differential equations in graded algebras, Nonassociative Algebra and Its Application (S. Gonzalez, ed.), Mathematics and its Applications #303, Kluwer Academic Publishers, 1994, pp. 179-182. MR 96f:17004
- 3.
- N. C. Hopkins and M. K. Kinyon, Automorphism eigenspaces of quadratic differential equations and qualitative theory, Diff. Eqs. and Dynamical Systems 5 (1997), 121-138. CMP 99:04
- 4.
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- 5.
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- 6.
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- 7.
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- 8.
- L. Markus, Quadratic differential equations and non-associative algebras, Contributions to the Theory of Nonlinear Oscillations, Vol. V (L. Cesari, J. P. LaSalle, and S. Lefschetz, eds.), Princeton Univ. Press, Princeton, 1960, pp. 185-213. MR 24:A2580
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- 10.
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- 11.
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Additional Information:
Nora
C.
Hopkins
Affiliation:
Department of Mathematics and Computer Science, Indiana State University, Terre Haute, Indiana 47809
Email:
hopkins@laurel.indstate.edu
Michael
K.
Kinyon
Affiliation:
Department of Mathematics and Computer Science, Indiana University South Bend, South Bend, Indiana 46634
Email:
mkinyon@iusb.edu
DOI:
10.1090/S0002-9947-99-02212-6
PII:
S 0002-9947(99)02212-6
Received by editor(s):
October 1, 1996
Received by editor(s) in revised form:
June 2, 1997
Posted:
July 19, 1999
Copyright of article:
Copyright
1999,
American Mathematical Society
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