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

MathSciNet review:
695272

Full-text PDF Free Access

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.

**[1]**George D. Birkhoff,*Proof of Poincaré’s geometric theorem*, Trans. Amer. Math. Soc.**14**(1913), no. 1, 14–22. MR**1500933**, 10.1090/S0002-9947-1913-1500933-9**[2]**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****[3]**Marston Morse,*George David Birkhoff and his mathematical work*, Bull. Amer. Math. Soc.**52**(1946), 357–391. MR**0016341**, 10.1090/S0002-9904-1946-08553-5**[4]**Howard Jacobowitz,*Periodic solutions of 𝑥′′+𝑓(𝑥,𝑡)=0 via the Poincaré-Birkhoff theorem*, J. Differential Equations**20**(1976), no. 1, 37–52. MR**0393673****[5]**Tung Ren Ding,*An infinite class of periodic solutions of periodically perturbed Duffing equations at resonance*, Proc. Amer. Math. Soc.**86**(1982), no. 1, 47–54. MR**663864**, 10.1090/S0002-9939-1982-0663864-1**[6]**Wei Yue Ding,*Fixed points of twist mappings and periodic solutions of ordinary differential equations*, Acta Math. Sinica**25**(1982), no. 2, 227–235 (Chinese). MR**677834**

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:
http://dx.doi.org/10.1090/S0002-9939-1983-0695272-2

Article copyright:
© Copyright 1983
American Mathematical Society