Hydrogen Atom in Strong Magnetic Fields: Regular and Irregular Motions

The stochastic transition in the classical Hamilton System describing the hydrogen atom in a strong magnetic field is observed by means of Poincaré mappings, and discussed in the framework of the gênerai theory of tori destruction. The existence of the third intégral in the regular région below the critical energy can explain the exponentially small séparations at avoided crossings of the energy levels, while the stochastic motion above the critical energy accounts for the irreqular structure of the spectrum in the inter-n-mixing régime. The regularity of the quasiLandau résonances corresponds to the existence of the adiabatic invariants above the escape energy.