Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Quadratic differential equations in $\mathbb {Z}_2$-graded algebras
HTML articles powered by AMS MathViewer

by Nora C. Hopkins and Michael K. Kinyon PDF
Trans. Amer. Math. Soc. 351 (1999), 4545-4559 Request permission

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
  • A. Brauer and C. Noel, Qualitative Theory of Ordinary Differential Equations, Dover Press, 1970.
  • Nora C. Hopkins, Quadratic differential equations in graded algebras, Non-associative algebra and its applications (Oviedo, 1993) Math. Appl., vol. 303, Kluwer Acad. Publ., Dordrecht, 1994, pp. 179–182. MR 1338177
  • 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.
  • Michael K. Kinyon, Quadratic differential equations on graded structures, Non-associative algebra and its applications (Oviedo, 1993) Math. Appl., vol. 303, Kluwer Acad. Publ., Dordrecht, 1994, pp. 215–218. MR 1338183
  • Michael K. Kinyon and Arthur A. Sagle, Quadratic dynamical systems and algebras, J. Differential Equations 117 (1995), no. 1, 67–126. MR 1320184, DOI 10.1006/jdeq.1995.1049
  • Michael K. Kinyon and Arthur A. Sagle, Automorphisms and derivations of differential equations and algebras, Rocky Mountain J. Math. 24 (1994), no. 1, 135–154. 20th Midwest ODE Meeting (Iowa City, IA, 1991). MR 1270032, DOI 10.1216/rmjm/1181072457
  • M. K. Kinyon and S. Walcher, Ordinary differential equations admitting a finite linear group of symmetries, J. Math. Anal. Appl. 216 (1997), 180–196.
  • Lawrence Markus, Quadratic differential equations and non-associative algebras, Contributions to the theory of nonlinear oscillations, Vol. V, Princeton Univ. Press, Princeton, N.J., 1960, pp. 185–213. MR 0132743
  • Arthur A. Sagle and Ralph E. Walde, Introduction to Lie groups and Lie algebras, Pure and Applied Mathematics, Vol. 51, Academic Press, New York-London, 1973. MR 0360927
  • Richard D. Schafer, An introduction to nonassociative algebras, Pure and Applied Mathematics, Vol. 22, Academic Press, New York-London, 1966. MR 0210757
  • Sebastian Walcher, Algebras and differential equations, Hadronic Press Monographs in Mathematics, Hadronic Press, Inc., Palm Harbor, FL, 1991. MR 1143536
Similar Articles
Additional Information
  • Nora C. Hopkins
  • Affiliation: Department of Mathematics and Computer Science, Indiana State University, Terre Haute, Indiana 47809
  • MR Author ID: 217047
  • Email: hopkins@laurel.indstate.edu
  • Michael K. Kinyon
  • Affiliation: Department of Mathematics and Computer Science, Indiana University South Bend, South Bend, Indiana 46634
  • MR Author ID: 267243
  • ORCID: 0000-0002-5227-8632
  • Email: mkinyon@iusb.edu
  • Received by editor(s): October 1, 1996
  • Received by editor(s) in revised form: June 2, 1997
  • Published electronically: July 19, 1999
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 351 (1999), 4545-4559
  • MSC (1991): Primary 34C35, 17A60, 34C20, 17A36
  • DOI: https://doi.org/10.1090/S0002-9947-99-02212-6
  • MathSciNet review: 1475685