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Generic bifurcations of the twist coefficient

Published online by Cambridge University Press:  19 September 2008

Richard Moeckel
Richard Moeckel
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
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Abstract

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We study the behavior of the twist coefficient near an elliptic fixed point for a one-parameter family of area-preserving diffeomorphisms. By looking at the singularities near resonance we can explain the sign changes which are typically found in such a family.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 1 , March 1990 , pp. 185 - 195
Copyright
Copyright © Cambridge University Press 1990

References

REFERENCES

[Ar]Arnold, V.. Mathematical Methods of Classical Mechanics. Appendix 7, Springer-Verlag: New York, 1978.Google Scholar
[Dep]Deprit, A. & Deprit-Bartolomé, A.. Stability of the triangular Lagrangian points. Astron. J. 72 (1967), 173–179.Google Scholar
[Mey]Meyer, K.. Generic bifurcation of periodic points. Trans. Amer. Math. Soc. 149 (1970), 95–107;Google Scholar
Generic Bifurcations in Hamiltonian Systems, Dynamical Systems, Warick 1974, Lecture Notes in Mathematics, pp. 62–70. Springer-Verlag: New York, 1975.Google Scholar
[Mos]Moser, J.. Lectures on Hamiltonian systems. Mem. Amer. Math. Soc. 81 (1968), 1–60.Google Scholar
[W]Wan, Y. H.. Computations of the stability condition forthe Hopf bifurcation of diffeomorphisms of R2. SIAM J. Appl. Math. 34 (1978), 167–175.Google Scholar