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On Sums of Vector Fields

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Abstract

We discuss one case where the integration of a sum of vector fields is reducible to the integration of the summands. Applications include the construction of a class of additive group actions on affine space and a proof that these are stably tame, and also the explicit solution of a class of differential equations from mathematical biology.

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References

  1. G. Andreoli: Algebre non associative e sistemi differenziati di Riccati in un problema di Genetica. Ann. Mat. Pura Appl. 49, 97–116 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  2. H. Bass: A non-triangular action of Ga on A3. J. Pure Appl. Algebra 33 1–5 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  3. K.-T. Chen: Decomposition of differential equations. Math. Annalen 146, 263–278 (1962)

    Article  MATH  Google Scholar 

  4. D. Daigle: A necessary and sufficient condition for triangulability of derivations of k[X, Y, Z]. Preprint, 8 pp. (1995)

  5. D. Daigle, G. Freudenburg: Locally nilpotent derivations over a UFD and an application to rank two locally nilpotent derivations of k[X1, …, Xn]. Preprint, 17 pp. (1994)

  6. D. Finston, S. Walcher: Centralizers of locally nilpotent derivations. To appear in J. Pure Appl. Algebra.

  7. D. Finston, S. Walcher: On a class of additive group actions on affine 3-space. To be published.

  8. L. Markus: Quadratic differential equations and nonassociative algebras. Ann. Math. Studies 45, 185-213, Princeton University Press (1960)

  9. P. J. Olver: Applications of Lie groups to differential equations. Springer, New York - Heidelberg - Berlin (1986)

    Book  MATH  Google Scholar 

  10. V. Popov: On actions of Ga on An. In: Algebraic groups (Utrecht 1986), Springer Lecture Notes in Mathematics 1271 (1987)

  11. M. K. Smith: Stably tame automorphisms. J. Pure Appl. Algebra 58, 209–212 (1989)

    Google Scholar 

  12. S. Walcher: Algebras and differential equations. Hadronic Press, Palm Harbor (1991)

    Google Scholar 

  13. S. Walcher: On Bernstein algebras which are train algebras. Proc. Edinburgh Math. Soc. 35, 159–166 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  14. A. Wörz-Busekros: Algebras in genetics. Springer Lecture Notes in Biomathematics 36 (1980)

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Walcher, S. On Sums of Vector Fields. Results. Math. 31, 161–169 (1997). https://doi.org/10.1007/BF03322158

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