Normally hyperbolic invariant manifolds phase-space structure

Phase-space structure of Hamiltonian systems with multiple degrees of freedom—in particular, normally hyperbolic invariant manifolds (NHlMs), intersections between their stable and unstable manifolds, and the Arnold web. 

Because the perturbation is Hamiltonian, the 3D level energy surfaces are preserved. In the 4D normally hyperbolic invariant manifold of the unperturbed space, the locally stable and unstable manifolds and the flow describe the geometric structure of the perturbed phase space given by the perturbed normally hyperbolic locally invariant manifold, the locally stable and unstable manifolds, and the persistence of the 2D nonresonant invariant tori T-,(Pi,P2)-... 

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