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On a topological property of globally canonical maps in classical mechanics

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Collected Works

Part of the book series: Vladimir I. Arnold - Collected Works ((ARNOLD,volume 1))

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Summary

The inequalities of M. Morse on the number of critical points of a function on a manifold are used in order to find the periodic solutions of the problems of mechanics.

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References

  1. Arnold, V.: Small denominators and problems of stability of motion in classical and celestial mechanics. Russian Math. Surveys, 6, 91–192 (1963)

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  2. Birkhoff, G. D.: Dynamical Systems. New-York (1927)

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  3. Milnor, J.: Morse Theory. Princeton University Press, Princeton (1963)

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  4. Poincaré, H.: Sur un théorème de géométrie. Rend. Circ. Math. Palermo, 33, 375–407 (1912)

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  5. Siegel, C. L.: Vorlesungen über Himmelsmechanik. Springer-Verlag, Berlin-Göttingen- Heidelberg (1956)

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© 2009 Springer-Verlag Berlin Heidelberg

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(2009). On a topological property of globally canonical maps in classical mechanics. In: Givental, A., et al. Collected Works. Vladimir I. Arnold - Collected Works, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01742-1_32

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