Generic bifurcation of periodic points
Author:
K. R. Meyer
Journal:
Trans. Amer. Math. Soc. 149 (1970), 95-107
MSC:
Primary 34.65
DOI:
https://doi.org/10.1090/S0002-9947-1970-0259289-X
MathSciNet review:
0259289
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Abstract | References | Similar Articles | Additional Information
Abstract: This paper discusses the bifurcation of periodic points of a generic symplectic diffeomorphism of a two manifold that depends on a parameter. A complete classification of the types of bifurcation that can occur in the generic case is given.
- [1] S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747–817. MR 228014, https://doi.org/10.1090/S0002-9904-1967-11798-1
- [2] A. Deprit and J. Henrard, A manifold of periodic orbits, Advances in Astronomy and Astrophysics 6 (1968).
- [3] Julian I. Palmore, Bridges and natural centers in the restricted three body problem, Center for Control Sciences, University of Minnesota, Minneapolis, Minn., 1969. MR 0282570
- [4] M. M. Peixoto, On an approximation theorem of Kupka and Smale, J. Differential Equations 3 (1967), 214–227. MR 209602, https://doi.org/10.1016/0022-0396(67)90026-5
- [5] C. Robinson, A global approximation theorem for Hamiltonian systems, Proc. Summer Inst. Global Analysis, (to appear).
- [6] H. Poincaré, Les méthodes nouvelles de la mécanique céleste, Tome 3, Gauthier-Villars, Paris, 1899.
- [7] George D. Birkhoff, Dynamical systems, With an addendum by Jurgen Moser. American Mathematical Society Colloquium Publications, Vol. IX, American Mathematical Society, Providence, R.I., 1966. MR 0209095
- [8] H. Levine, Singularities of differentiable mappings. I, Mathematisches Institute der Universität, Bonn, 1959.
- [9] Harold I. Levine, The singularities, 𝑆₁^{𝑞}, Illinois J. Math. 8 (1964), 152–168. MR 0159343
- [10] Harry Pollard, Mathematical introduction to celestial mechanics, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1966. MR 0197175
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1970-0259289-X
Keywords:
Generic,
Baire space,
Baire category,
symplectic diffeomorphism,
periodic points,
Hamiltonian differential equations,
bifurcation,
stability
Article copyright:
© Copyright 1970
American Mathematical Society