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The dynamics of a charged particle in a relativistic strong electromagnetic plane wave propagating in vacuum is studied first, the problem is shown to be integrable when the wave propagates in vacuum. One particle in a high-intensity wave, propagating in a vacuum, perturbed by a low-intensity traveling wave is considered next. Resonances are identified, and conditions for resonance overlap are studied. Stochastic acceleration is shown by considering a single particle. It is confirmed in plasma in realistic situations with particle-in-cell code simulations. Finally, it is shown that when considering a low-density plasma interacting with a high-intensity wave perturbed by a low-intensity counterpropagating wave, stochastic heating can provide electrons with the right momentum for trapping in the wakefield and efficient acceleration.