  The radiation reaction radically influences the electron motion in an
electromagnetic standing wave formed by two super-intense counter-propagating
laser pulses. Depending on the laser intensity and wavelength, either classical
or quantum mode of radiation reaction prevail, or both are strong. When
radiation reaction dominates, electron motion evolves to limit cycles and
strange attractors. This creates a new framework for high energy physics
experiments on an interaction of energetic charged particle beams and colliding
super-intense laser pulses.
