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The invariance of Poincaré’s generating function for canonical transformations. (English) Zbl 0235.70008

##### MSC:
 70H15 Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics 70F15 Celestial mechanics
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##### References:
 [1] Abraham, R., Marsden, J.: Foundations of mechanics. New York: W. A. Benjamin 1967. [2] Meyer, K. R.: Generic bifurcation of periodic points. Trans. Amer. Math. Soc.149, 95–107 (1970). · Zbl 0198.42902 [3] Poincaré, H.: Les méthodes nouvelles de la mécanique céleste, vol. 3. Paris: Gauthier-Villars 1892. [4] Tougeron, J.-Cl.: Idéaux de fonctions differentiables I. Ann. Inst. Fourier, Grenoble18, 177–240 (1968). · Zbl 0188.45102 [5] Wall, C. T. C.: Lectures onC stability and classification. In: Proceedings of Liverpool Singularities-Symposium. I, pp. 178–206. Berlin-Heidelberg-New York: Springer 1971. [6] Weinstein, A.: Perturbation of periodic manifolds of hamiltonian systems. Bull. Amer. Math. Soc.77, 814–818 (1971). · Zbl 0218.58006 [7] Weinstein, A.: Periodic orbits of hamiltonian systems via critical point theory (to appear). [8] Weinstein, A.: Symplectic structures on Banach manifolds. Bull. Amer. Math. Soc.75, 1040–1041 (1969). · Zbl 0179.50104 [9] Weinstein, A.: Symplectic manifolds and their lagrangian submanifolds. Advances in Math.3, 329–346 (1971). · Zbl 0213.48203
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