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 note on the rotation number of Poincaré

Author: Shu Xiang Yu
Journal: Proc. Amer. Math. Soc. 89 (1983), 618-622
MSC: Primary 34C40
MathSciNet review: 718984
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The present note gives a formula relating the rotation number, the conjugating function and the vector field for a flow on a torus. Furthermore, in a particular case, it gives a formula such that the rotation number $\rho$ can be computed only by means of the vector field $f(x,y)$.

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

    A. Denjoy, Sur les courbes defines par les équations différentielles á la surface du tore, J. Math. Pures Appl. 11 (1932), 333-375.
  • Jack K. Hale, Ordinary differential equations, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1969. Pure and Applied Mathematics, Vol. XXI. MR 0419901
  • Shlomo Sternberg, On differential equations on the torus, Amer. J. Math. 79 (1957), 397–402. MR 86228, DOI

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34C40

Retrieve articles in all journals with MSC: 34C40

Additional Information

Keywords: Rotation number, conjugating function, ergodic
Article copyright: © Copyright 1983 American Mathematical Society