Pacific Journal of Mathematics

The Campbell-Hausdorff group and a polar decomposition of graded algebra automorphisms.

A. Baider and R. C. Churchill

Article information

Pacific J. Math., Volume 131, Number 2 (1988), 219-235.

First available in Project Euclid: 8 December 2004

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 17B70: Graded Lie (super)algebras
Secondary: 16A03 58F99


Baider, A.; Churchill, R. C. The Campbell-Hausdorff group and a polar decomposition of graded algebra automorphisms. Pacific J. Math. 131 (1988), no. 2, 219--235.

Export citation


  • [1] N. Bourbaki, Commutative Algebra, Hermann,Paris, and Addison-Wesley, Reading, MA., 1973.
  • [2] C. Bouton, Bull. Amer. Math. So, 23 (1916), p. 73.
  • [3] A. Brjuno, The analytical form of differential equations, Trans. Moscow Math. Soc, 25 (1971), 131-288.
  • [4] H. Broer, Formal normal form theorems for vector fields and some consequences to bifurcations in the volume preserving case, in Dynamical Systems and Turbulence, Warwick, 1980 (D. A. Rand and L.-S. Young, Eds.), Springer Lecture Notes in Mathematics, Vol. 898, Springer-Verlag, New York, 1981.
  • [5] P. Dixon and J. Esterle, Michael's problem and the Poincare-Fatou-Bieberbach phenomenon, Bull. Amer. Math. Soc, 15 (1986), 127-188.
  • [6] R. Gerard and A. H. M. Levelt, Sur les connexions a singularites regulieres dans le cas deplusiers variables, Funcialaj Elevacioj, 19 (1976), 149-173.
  • [7] G. Hochschild, Basic Theory of Algebraic Groups and Lie Algebras, Springer-Verlag, New York, 1981.
  • [8] D. Lewis, On formal power series transformations, Duke J. Math., 5 (1939), 794-803.
  • [9] J. Moser, Lectures on Hamiltonian systems, Mem. Amer. Math. Soc, No. 81, Amer. Math. Soc, Providence, RL, 1968.
  • [10] J. P. Serre, Lie Algebras and Lie Groups, W. A. Benjamin, New York, 1965.
  • [11] S. Sternberg, Infinite Lie groups and theformal aspects of dynamical systems, J. Math. Mech., 10 (1961), 451-474.
  • [12] F. Takens, Singularities of vectorfields, In: Publ. Math. IHES, 43 (1974), 48-100.
  • [13] F. Takens, Forced oscillations and bifurcations, in Applications of Global Analysis I, Comm. of the Math. Inst. Rijksuniversiteit Utrecht, 1974.
  • [14] J. van der Meer, The Hamiltonian Hopf Bifurcation, Springer Lecture Notes in Mathematics, Vol. 1160, Springer-Verlag, New York, 1985.