The ionization of atoms in a low-frequency linearly polarized electromagnetic field (the photon energy is much lower than the ionization potential of an atom) is considered under new conditions, in which the Coulomb interaction of an electron with the atomic core in the final state of the continuum cannot be considered in perturbation theory in the interaction of the electron with the electromagnetic field. The field is assumed to be much weaker that the atomic field. In these conditions, the classical motion of the electron in the final state of the continuum becomes chaotic (so-called dynamic chaos). Using the well-known Chirikov method of averaging over chaotic variations of the phase of motion, the problem can be reduced to non-linear diffusion on the energy scale. We calculate the classical electron energy in the final state, which is averaged over fast chaotic oscillations and takes into account both the Coulomb field and the electromagnetic field. This energy is used to calculate the probability of ionization from the ground state of the atom to a lower-lying state in the continuum using the Landau-Dykhne approximation (to exponential accuracy). This ionization probability noticeably depends on the field frequency. Upon a decrease in frequency, a transition to the well-known tunnel ionization limit with a probability independent of the field frequency is considered.
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