A note on the rotation number of Poincaré
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- by Shu Xiang Yu
- Proc. Amer. Math. Soc. 89 (1983), 618-622
- DOI: https://doi.org/10.1090/S0002-9939-1983-0718984-0
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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
- 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, Pure and Applied Mathematics, Vol. XXI, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1969. MR 0419901
- Shlomo Sternberg, On differential equations on the torus, Amer. J. Math. 79 (1957), 397–402. MR 86228, DOI 10.2307/2372688
Bibliographic Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 89 (1983), 618-622
- MSC: Primary 34C40
- DOI: https://doi.org/10.1090/S0002-9939-1983-0718984-0
- MathSciNet review: 718984