The numerical search for the internal dynamics of NHIMs and their pictorial representation

Abstract

The topic of this article is the numerical search of codimension 2 Normally Hyperbolic Invariant Manifolds (NHIM) in Hamiltonian systems with 3 degrees of freedom and their internal dynamics. We point out relations between different strategies to find such surfaces numerically. We can start from index-1 saddles of the effective potential or from a partially integrable case and follow the NHIM along some curve in the parameter space of the system. Or, we can look for the stable and unstable manifolds of such surfaces by an appropriate indicator method. We show numerical examples for an electron moving in a perturbed magnetic dipole field.