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

Abstract

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 $O({\epsilon }^2)$.

8 pages, LaTeX

Cited by in corpus (2)

• Numerical test for hyperbolicity of chaotic dynamics in time-delay systems
• Numerical test for hyperbolicity in chaotic systems with multiple time delays