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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on the rotation number of Poincaré
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by Shu Xiang Yu PDF
Proc. Amer. Math. Soc. 89 (1983), 618-622 Request permission

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
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Additional 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