Nonintegrable dynamical systems have complex structures in their phase space.Motion of a test charged particle in a dipole magnetic field can be reduced to a 2degree-of-freedom (2 d.o.f.) nonintegrable Hamiltonian system. We carried out asystematicstudyoforbitsofchargedparticleswithanazimuthalinitialvelocityina dipole field via calculation of their Lyapunov characteristic exponents (LCEs)and escape times for a dimensionless energy less and greater than 1/32, respec-tively. Meridian plane periodic orbits symmetric with respect to the equatorialplane are then identified. We found that 1) symmetric periodic orbits can be clas-sified into several classes based on their number of crossing points on the equato-rialplane;2)theinitialconditionsoftheseclasseslocateonclosedloopsorclosedcurves going through the origin; 3) most isolated regions of stable quasi-periodicorbits are associated asymmetric stable periodic orbits; 4) classes of asymmet-ric periodic orbits either go through the origin or terminate at flat equatorialplane orbits with the other end approaching centers of spiral structures; 5) thereare apparent self-similarities in the above features with the decrease of energy.
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