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A note on the rotation number of Poincaré


Author: Shu Xiang Yu
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
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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 [Enhancements On Off] (What's this?)

  • [1] A. Denjoy, Sur les courbes defines par les équations différentielles á la surface du tore, J. Math. Pures Appl. 11 (1932), 333-375.
  • [2] Jack K. Hale, Ordinary differential equations, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1969. Pure and Applied Mathematics, Vol. XXI. MR 0419901
  • [3] Shlomo Sternberg, On differential equations on the torus, Amer. J. Math. 79 (1957), 397–402. MR 0086228, https://doi.org/10.2307/2372688

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0718984-0
Keywords: Rotation number, conjugating function, ergodic
Article copyright: © Copyright 1983 American Mathematical Society