Symplectic Diffeomorphisms with Infinitely Many elliptic Periodic Points

摘要

Let M be a compact manifold of dimension greater than one. Let A_f=2). Suppose P is a hyperbolic periodic point of f in A_f with period k, detT_pf~k<1, dimW~u(p,f)=1, W~s(p,f) and W~u(p,f) have a point of tangency. Newhouse [1] shows that there exists a residual subset ξ of a neighborhood N of f such that for each g∈ξ, g has infinitely many sinks. Later, on basis of the conclusion of Takens, new house also proved that for a compact symplectic manifold M, there exists a Residual subset ξ