1. “Irregular” here means chaotic in the sense of exponentially unstable for finite times, as opposed to infinite times (see e.g., T. Tel, “Transient chaos’, to be published in ’Directions in Chaos, Vol. 3’, Bai-Lin Hao (ed.), World Scientific, Singapore). This is numerically proven for the system discussed in this chapter by calculating the Liapunov exponents in [3] for the Kepler map that is believed to be a good approximation of the 1D-ordinary differential equation model of a hydrogen atom in a microwave field.
2. Moorman L., Koch P.M. (1991) ’Microwave ionization of Rydberg atoms’, Bai-Lin Hao, Da Hsuan Feng, Jian-Min Yuan (eds.), Directions in Chaos, Vol. 4, World Scientific, Singapore, Ch 2, to appear.
3. HafFmans, A.F., Moorman, L., Rabinovitch, A., and Koch, P.M., ’Initial condition phase space stability pictures of two dimensional area preserving maps’, in preperation
4. Leeuwen K.A.H. van, Oppen G. v., Renwick S., Bowlin J.B., Koch P.M., Jensen R.V., Rath O., Richards D., and Leopold J.G. (1985) ‘Microwave ionization of hydrogen atoms: Experiment versus classical dynamics’, Phys. Rev. Lett. 55, 2231–4
5. Casati G., Chirikov B.V., Shepelyansky D.L. (1984) ’Quantum limitation for chaotic excitation of the hydrogen atom in a monochromatic field’, Phys. Rev. Lett. 53, 2525–28