Duke Mathematical Journal

The relationship between the index of a strongly stable periodic linear Hamiltonian vectorfield and the index of its stability domain

Richard Cushman

Article information

Source
Duke Math. J., Volume 45, Number 4 (1978), 701-709.

Dates
First available in Project Euclid: 20 February 2004

https://projecteuclid.org/euclid.dmj/1077313094

Digital Object Identifier
doi:10.1215/S0012-7094-78-04532-5

Mathematical Reviews number (MathSciNet)
MR518101

Zentralblatt MATH identifier
0403.58003

Subjects
Primary: 58F05
Secondary: 34C35 70H99: None of the above, but in this section

Citation

Cushman, Richard. The relationship between the index of a strongly stable periodic linear Hamiltonian vectorfield and the index of its stability domain. Duke Math. J. 45 (1978), no. 4, 701--709. doi:10.1215/S0012-7094-78-04532-5. https://projecteuclid.org/euclid.dmj/1077313094

References

• [1] J. J. Duistermaat, On the Morse index in variational calculus, Advances in Math. 21 (1976), no. 2, 173–195.
• [2] J. J. Duistermaat, Fourier integral operators, Courant Institute of Mathematical Sciences New York University, New York, 1973.
• [3] I. M. Gel'fand and V. B. Lidskiĭ, On the structure of the regions of stability of linear canonical systems of differential equations with periodic coefficients, Amer. Math. Soc. Transl. (2) 8 (1958), 143–181.
• [4] M. G. Kreĭ n, The basic propositions of the theory of $\lambda$-zones of stability of a canonical system of linear differential equations with periodic coefficients, In memory of Aleksandr Aleksandrovič Andronov, Izdat. Akad. Nauk SSSR, Moscow, 1955, pp. 413–498.
• [5] R. Cushman and J. J. Duistermaat, The behavior of the index of a periodic linear Hamiltonian system under iteration, Advances in Math. 23 (1977), no. 1, 1–21.
• [6] J. V. Ralston, On the construction of quasimodes associated with stable periodic orbits, Comm. Math. Phys. 51 (1976), no. 3, 219–242.