Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Generic stability properties of periodic points


Author: K. R. Meyer
Journal: Trans. Amer. Math. Soc. 154 (1971), 273-277
MSC: Primary 34.51
DOI: https://doi.org/10.1090/S0002-9947-1971-0271490-9
MathSciNet review: 0271490
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A classification of the periodic points of a generic area-perserving diffeomorphism which depends on a parameter is given. The stability properties of each periodic point in the classification is decided.


References [Enhancements On Off] (What's this?)

  • [1] G. D. Birkhoff, Dynamical systems, Amer. Math. Soc. Colloq. Publ., vol. 9, Amer. Math. Soc., Providence, R. I., 1927; rev. ed., 1966. MR 35 #1. MR 0209095 (35:1)
  • [2] P. Hartman, Ordinary differential equations, Wiley, New York, 1964. MR 30 #1270. MR 0171038 (30:1270)
  • [3] K. R. Meyer, Generic bifurcation of periodic points, Trans. Amer. Math. Soc. 149 (1970), 95-107. MR 0259289 (41:3931)
  • [4] J. Moser, On invariant curves of area-preserving mappings of an annulus, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II, 1962, 1-20. MR 26 #5255. MR 0147741 (26:5255)
  • [5] C. L. Siegel, Vorlesungen über Himmelsmechanik, Springer-Verlag, Berlin, 1956. MR 18, 178. MR 0080009 (18:178c)
  • [6] D. L. Slotnick, Asymptotic behavior of solutions of canonical systems near a closed, unstable orbit. Contributions to the theory of nonlinear oscillations. Vol. IV, Ann. of Math. Studies, no. 41, Princeton Univ. Press, Princeton, N. J., 1958, pp. 85-110. MR 21 #166. MR 0101354 (21:166)
  • [7] E. T. Whittaker and G. N. Watson, A course in modern analysis, 4th ed., Cambridge Univ. Press, New York, 1940.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 34.51

Retrieve articles in all journals with MSC: 34.51


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0271490-9
Keywords: Generic, Baire category, area-preserving, symplectic, stability, periodic point
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society