Let M be a smooth differentiable manifold, and f a C’diffeomorphism. Suppose that p∈M is a hyperbolic fixed point of f. According to the well-known stable manifold theorem, W^u(p) and W^s(p) are C^r submanifolds of ...Let M be a smooth differentiable manifold, and f a C’diffeomorphism. Suppose that p∈M is a hyperbolic fixed point of f. According to the well-known stable manifold theorem, W^u(p) and W^s(p) are C^r submanifolds of M. The λ-lemma stated below gives a property of W^u(p) and W^s(p), which characterizes W^u(p) and W^s(p) powerfully in many cases when transversality appears.展开更多
文摘Let M be a smooth differentiable manifold, and f a C’diffeomorphism. Suppose that p∈M is a hyperbolic fixed point of f. According to the well-known stable manifold theorem, W^u(p) and W^s(p) are C^r submanifolds of M. The λ-lemma stated below gives a property of W^u(p) and W^s(p), which characterizes W^u(p) and W^s(p) powerfully in many cases when transversality appears.
