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References
Sur un théorème de Géométrie, Rendiconti del Circolo Matematico di Palermo, vol. 33, 1912.
An Extension of Poincarés Last Geometric Theorem, Acta Mathematica, vol. 47, 1926.
See my paper, “Dynamical Systems With Two Degrees of Freedom”, Transactions of the American Mathematical Society, vol. 18, 1917. It is assumed that the Lagrangian prineipal functionL is quadratic in the velocities.
See my paperOn the Restricted Problem of Three Bodies, Rendiconti del Circolo Matematieo di Palermo, vol. 39, 1915, and the paper of Poincaré cited above.
See my recentActa article (loc. cit.). By the index of an invariant point is meant the total changes in angular direction of a line joining a pointP to its imageP 1 whenP makes a small positive circuit of the invariant point.
See my paper in theRendiconti di Palermo, loc. cit. Rendiconti del Circolo Matematieo di Palermo, vol. 39, 1915, and the paper of Poincaré cited above.
See my earlier articleSurface Transformations and Their Dynamical Applications, Acta Mathematica, vol. 43, 1922.
See my earlierActa article. A system is transitive if motions can be found passing from nearly one assigned state to nearly any other arbitrarily assigned state. This property is probably satisfied “in general» by non-integrable dynamical systems.
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Birkhoff, G.D. On the periodic motions of dynamical systems. Acta Math. 50, 359–379 (1927). https://doi.org/10.1007/BF02421325
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DOI: https://doi.org/10.1007/BF02421325