Introduction to Hamiltonian dynamical systems and the n-body problem j Kenneth R. Meyer, Glen R. Hali. p. cm.-(Applied mathematical sciences; v. 90) Includes bibliographical references and index.

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Abstract. This paper discusses the bifurcation of periodic points of a generic symplectic diffeomorphism of a two manifold that depends on a parameter. A complete classification of the types of bifurcation that can occur in the generic case is given.Introduction. This paper discusses the bifurcation of periodic points of an area preserving diffeomorphism that depends on a parameter. In the spirit of Thorn and Smale only the generic case is considered. As in Smale's work on discrete dynamical systems the present problem was suggested by problems in ordinary differential equations (see [1]). Whereas Smale modeled his theory on differential equations with dissipation the present problem was suggested by conservative differential equations.Throughout this paper smooth will always mean C°°. Let M be a smooth, compact, two dimensional, symplectic manifold, S=SX the circle considered as a smooth manifold and F the space of all smooth mappings M with the property that for each s e S the map M is a symplectic diffeomorphism. Let F have the usual topology of C°° maps. The space F is complete and therefore is a Baire space. A point (x, s) e M x S is called a periodic point of least period m if

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