The Intersection Angles between N-Dimensional Stable and Unstable Manifolds in 2N-Dimensional Symplectic Mappings

Details The Intersection Angles between N-Dimensional Stable and Unstable Manifolds in 2N-Dimensional Symplectic Mappings The Intersection Angles between N-Dimensional Stable and Unstable Manifolds in 2N-Dimensional Symplectic Mappings

1999-06-14

arxiv.org/abs/chao-dyn/9906021v1

Nonlinear Sciences

Chaotic Dynamics

8 pages, LaTeX

Scientific paper

10.1143/PTP.102.701

We asymptotically compute the intersection angles between N-dimensional stable and unstable manifolds in 2N-dimensional symplectic mappings. There exist particular 1-dimensional stable and unstable sub-manifolds which experience exponentially small splitting of separatrix in our models. We show that the angle between the sub-manifolds is exponentially small with respect to the perturbation parameter $\epsilon$, and the other angles are $O(\epsilon^2)$.

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