The formal linearization of a semisimple Lie algebra of vector fields about a singular point
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- by Robert Hermann PDF
- Trans. Amer. Math. Soc. 130 (1968), 105-109 Request permission
Abstract:
A classical theorem by Poincaré gives conditions that a nonlinear ordinary differential equation \[ dx/dt = A(x),\] with $A(0) = 0$ in n variables $x = ({x_1}, \ldots ,{x_n})$ can be reduced to a linear form \[ \frac {{dx’}}{{dt}} = \frac {{\partial A}}{{\partial x}}(0)x’\] by a change of variables $x’ = f(x)$. A generalization is given for a finite set of such differential equations, which form a semisimple Lie algebra.References
- Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0143793
- Shlomo Sternberg, Local contractions and a theorem of Poincaré, Amer. J. Math. 79 (1957), 809–824. MR 96853, DOI 10.2307/2372437
Additional Information
- © Copyright 1968 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 130 (1968), 105-109
- MSC: Primary 22.90
- DOI: https://doi.org/10.1090/S0002-9947-1968-0217225-7
- MathSciNet review: 0217225