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)

 

 

Invariant manifolds for some autonomous systems


Author: F. S. Van Vleck
Journal: Trans. Amer. Math. Soc. 107 (1963), 186-196
MSC: Primary 57.48
DOI: https://doi.org/10.1090/S0002-9947-1963-0147732-2
MathSciNet review: 0147732
Full-text PDF Free Access

References | Similar Articles | Additional Information

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

  • [1] S. P. Diliberto, Perturbation theory of periodic surfaces. I, Tech. Rep. No. 24, Dept. of Math., Univ. of Calif., Berkeley, Calif., April, 1958.
  • [2] -, Perturbation theory of periodic surfaces. II, Tech. Rep. No. 9, Dept. of Math., Univ. of Calif., Berkeley, Calif., April, 1957.
  • [3] S. P. Diliberto and G. Hufford, Perturbation theorems for non-linear ordinary differential equations, Contributions to the theory of nonlinear oscillations, vol. 3, Annals of Mathematics Studies, no. 36, Princeton University Press, Princeton, N. J., 1956, pp. 207–236. MR 0083071
  • [4] George Hufford, Banach spaces and the perturbation of ordinary differential equations, Contributions to the theory of nonlinear oscillations, vol. 3, Annals of Mathematics Studies, no. 36, Princeton University Press, Princeton, N. J., 1956, pp. 173–195. MR 0083075
  • [5] Walter T. Kyner, A fixed point theorem, Contributions to the theory of nonlinear oscillations, vol. 3, Annals of Mathematics Studies, no. 36, Princeton University Press, Princeton, N. J., 1956, pp. 197–205. MR 0081472
  • [6] -, Invariant manifolds, Univ. of Southern Calif. Rep., Los Angeles, Calif., 1959.
  • [7] Walter T. Kyner, Small periodic perturbations of an autonomous system of vector equations, Contributions to the theory of nonlinear oscillations, Vol. IV, Annals of Mathematics Studies, no. 41, Princeton University Press, Princeton, N.J., 1958, pp. 111–124. MR 0101946
  • [8] Solomon Lefschetz, Differential equations: Geometric theory, Second edition. Pure and Applied Mathematics, Vol. VI, Interscience Publishers, a division of John Wiley & Sons, New York-Lond on, 1963. MR 0153903
  • [9] Norman Levinson, Small periodic perturbations of an autonomous system with a stable orbit, Ann. of Math. (2) 52 (1950), 727–738. MR 0037974, https://doi.org/10.2307/1969445
  • [10] H. Poincaré, Les méthodes nouvelles de la mécanique céleste. Tome I. Solutions périodiques. Non-existence des intégrales uniformes. Solutions asymptotiques, Dover Publications, Inc., New York, N.Y., 1957 (French). MR 0087812

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57.48

Retrieve articles in all journals with MSC: 57.48


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1963-0147732-2
Article copyright: © Copyright 1963 American Mathematical Society