Versal deformations of infinitesimally symplectic transformations with antisymplectic involutions
- 406 Downloads
Normal forms for versal unfoldings of linear Hamiltonian systems anti-commute with an anti-symplectic involution are given in this paper. They can be derived from suitable chosen versal unfoldings of linear Hamiltonians without an involution. The results are expressed in an alternative basis and in a symplectic basis compatible with this involution. Descriptions of unfoldings of codimension ≤ 2 are given for an illustration.
Unable to display preview. Download preview PDF.
- 2.Burgoyne, N. and Cushman, R., Normal forms for real linear Hamiltonian systems, The 1976 NASA Conference on Geometric Control Theory, pp. 483–529, Math. Sci. Press, Brookline, MA, 1977.Google Scholar
- 3.Galin, D. M., Versal deformations of linear Hamiltonian systems, Amer. Math. Soc. Transl. (2) vol. 118, 1982.Google Scholar
- 6.Mackay, R., Stability of equilibria of Hamiltonian systems, in Nonlinear Phenomena and Chaos (ed. S. Sarkar), Adam Hilges, Bristol, (1986), 254–270.Google Scholar
- 8.Nickerson, H. K., spencer, D. C., and Steenrod, N.E., Advanced Calculus.Google Scholar
- 9.Sevryuk, M. B., Reversible systems; Lecture Notes in Mathematics 1211; Springer-Verlag (1986).Google Scholar
- 10.Wan, Y. H., Normal forms for infinitesimally symplectic transformations with involutions. Preprint, State University of New York at Buffalo, 1989.Google Scholar