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References
Cherry, T.M., Analytic quasi-periodic curves of discontinuous type on a torus, Proceedings of the London Mathematical Society, vol. 44(1938), pp. 175–215.
Denjoy, Arnaud, Sur les courbes définies par les équations différentielles à la surface du tore, Journal de Mathématiques Pures et Appliquées, vol. 11(1932), pp. 333–375.
Hartman, Philip, Ordinary Differential Equations, Wiley, New York, 1964.
Kneser, Hellmuth, Reguläre Kurvenscharen auf den Ringflächen, Mathematische Annalen, vol. 91(1924), pp. 135–154.
Lima, Elon, L., Common sigularities of commuting vector fields on 2-manifolds, Commentarii Mathematici Helvetici, vol. 39(1964), pp. 97–110.
Maier, A.G., Trajectories on the closed orientable surfaces, Matematiceskii Sbornik, vol. 12(1943), pp. 71–84 (Russian. English summary).
Markley, Nelson G., The structure of flows on two-dimensional manifolds, Dissertation, Yale University, 1966.
Markley, Nelson G., The Poincaré-Bendixson theorem for the Klein bottle, transactions of the American Mathematical Society, vol. 135(1969), pp. 159–165.
Markley, Nelson G., A new type of non-trivial minimal set, University of Maryland Technical Report TR 69-78.
Markley, Nelson G., On the number of recurrent orbit closures, Proceedings of the American Mathematical Society (to appear).
Nemytskii, V.V., and Stepanov, V.V., Qualitative Theory of Differential Equations, Princeton Mathematical Series, no. 22, Princeton University Press, Princeton, 1960, (Translated from Russian).
Schwartz, Arthur J., A generalization of a Poincaré-Bendixson theorem to closed two-dimensional manifolds, American Journal of Mathematics, vol. 85(1963), pp. 453–458; errata, p. 753.
Siegel, Carl Ludwig, Note on differential equations on the torus, Annals of Mathematics, vol. 46(1945), pp. 423–428.
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Markley, N.G. (1970). Non-trivial minimal sets — a survey. In: Yorke, J.A. (eds) Seminar on Differential Equations and Dynamical Systems, II. Lecture Notes in Mathematics, vol 144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0059932
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DOI: https://doi.org/10.1007/BFb0059932
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