A generalization of the PoincaréBirkhoff theorem
Author:
Wei Yue Ding
Journal:
Proc. Amer. Math. Soc. 88 (1983), 341346
MSC:
Primary 54H20; Secondary 54H25, 58F12
MathSciNet review:
695272
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Abstract: A generalized form of the PoincaréBirkhoff theorem is proved. The generalization is useful for the further applications of this famous fixed point theorem.
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George
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Tung
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Wei
Yue Ding, Fixed points of twist mappings and periodic solutions of
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 [1]
 G. D. Birkhoff, Proof of Poincaré's geometric theorem, Trans. Amer. Math. Soc. 14 (1913), 1422. 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)
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 M. Morse, George David Birkhoff and his mathematical work, Bull. Amer. Math. Soc. 52 (1946), 357391. MR 0016341 (8:3f)
 [4]
 H. Jacobowitz, Periodic solutions of via the PoincaréBirkhoff Theorem, J. Differential Equations 20 (1976), 3752; and Corrigendum: The existence of the second fixed point: A correction to "Periodic solutions of via the PoincaréBirkhoff Theorem", J. Differential Equations 25 (1977), 148149. 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), 4754. MR 663864 (83j:34041)
 [6]
 W. Y. Ding, Fixed points of twist mappings and periodic solutions of ordinary differential equations, Acta Math. Sinica 25, 227235. (Chinese) MR 677834 (84d:58061)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198306952722
PII:
S 00029939(1983)06952722
Article copyright:
© Copyright 1983 American Mathematical Society
