Abstract
Often the first step in analyzing a given problem requires the transformation of the linearized system into its Jordan canonical form. If the given system depends on parameters, say e this reduction to Jordan canonical form can be an unstable operation, since the normal form and the transformation itself can depend in a discontinuous way on these parameters. The difficulty to which we elude occurs when several eigenvalues of the linearized system coincide, say for ε = 0. In the generic case the matrix will be non-semi-simple, i.e. not diagonalizable for ε = 0.
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References
V. Arnold, On matrices depending on parameters, Russian Math. Surveys, 26:29–43, 1971.
R. Cushman, A. Kelley, and H. Kocak, Versa! normal form at the Lagrangian equilibrium L 4 J. Differential Equations, 64:340–374, 1986.
F. R. Gantmacher, Matrizentheorie, Springer, 1986.
K. R. Meyer and D. S. Schmidt, Periodic orbits near L 4 for mass ratio’s near the critical mass ratio of Routh, Celestial Mech., 4:99–109, 1971.
D. S. Schmidt, Periodic solutions near a resonant equilibrium of a Hamilionian system, Celestial Mech., 9:81–103, 1974.
J. C. van der Meer, The Hamilionian Hopf Bifurcation, Springer, 1986.
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© 1991 Springer-Verlag New York Inc.
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Schmidt, D.S. (1991). Transformation to Versal Normal Form. In: Meyer, K.R., Schmidt, D.S. (eds) Computer Aided Proofs in Analysis. The IMA Volumes in Mathematics and Its Applications, vol 28. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9092-3_20
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DOI: https://doi.org/10.1007/978-1-4613-9092-3_20
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