Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A generalization of the Poincaré-Birkhoff theorem


Author: Wei Yue Ding
Journal: Proc. Amer. Math. Soc. 88 (1983), 341-346
MSC: Primary 54H20; Secondary 54H25, 58F12
DOI: https://doi.org/10.1090/S0002-9939-1983-0695272-2
MathSciNet review: 695272
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A generalized form of the Poincaré-Birkhoff theorem is proved. The generalization is useful for the further applications of this famous fixed point theorem.


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

  • [1] G. D. Birkhoff, Proof of Poincaré's geometric theorem, Trans. Amer. Math. Soc. 14 (1913), 14-22. MR 1500933
  • [2] G. D. Birkhoff, Dynamical systems, Amer. Math. Soc. Colloq. Publ., vol. 27, Amer. Math. Soc. Providence, R.I., 1927; revised 1966; reprinted 1979. MR 0209095 (35:1)
  • [3] M. Morse, George David Birkhoff and his mathematical work, Bull. Amer. Math. Soc. 52 (1946), 357-391. MR 0016341 (8:3f)
  • [4] H. Jacobowitz, Periodic solutions of $ x'' + f(x,t) = 0$ via the Poincaré-Birkhoff Theorem, J. Differential Equations 20 (1976), 37-52; and Corrigendum: The existence of the second fixed point: A correction to "Periodic solutions of $ x'' + f(x,t) = 0$ via the Poincaré-Birkhoff Theorem", J. Differential Equations 25 (1977), 148-149. MR 0393673 (52:14482)
  • [5] T. R. Ding, An infinite class of periodic solutions of periodically perturbed Duffing equations at resonance, Proc. Amer. Math. Soc. 86 (1982), 47-54. MR 663864 (83j:34041)
  • [6] W. Y. Ding, Fixed points of twist mappings and periodic solutions of ordinary differential equations, Acta Math. Sinica 25, 227-235. (Chinese) MR 677834 (84d:58061)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54H20, 54H25, 58F12

Retrieve articles in all journals with MSC: 54H20, 54H25, 58F12


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0695272-2
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society