| Abstract: |
| In this talk, we present the dynamical behavior of charged particles under the influence of the Earth`s magnetic field. This work focuses on the motion of the protons in the relativistic regime, analysing the topology of invariant spatial regions in two magnetic field models, namely, the dipolar and Luhmann tail configurations. We compute the distributions of escape and residence times, the exit basins, and the fractal dimensions of their boundaries, as well as a scaling law between the coefficient of the decay law and the energy of the protons. We also present a robust symplectic numerical scheme which is suitable for modeling trajectories where nonlinear effects and the presence of strong sensitivity to initial conditions are present. |
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