摘要

Let (M, Omega) be a smooth symplectic manifold and f : M -> M be a symplectic diffeomorphism of class C-l (l >= 3). Let N be a compact submanifold of M which is boundaryless and normally hyperbolic for f. We suppose that N is controllable and that its stable and unstable bundles are trivial. We consider a C-1-submanifold 1 of M whose dimension is equal to the dimension of a fiber of the unstable bundle of TNM. We suppose that 1 transversely intersects the stable manifold of N. Then, we prove that for all epsilon > 0, and for n is an element of N large enough, there exists x(n) is an element of N such that f(n) (Delta) is epsilon-close, in the C-1 topology, to the strongly unstable manifold of xn. As an application of this lambda-lemma, we prove the existence of shadowing orbits for a finite family of invariant minimal sets (for which we do not assume any regularity) contained in a normally hyperbolic manifold and having heteroclinic connections. As a particular case, we recover classical results on the existence of diffusion orbits (Arnold's example).

  • 出版日期2015-10