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In this report, we present a dynamical systems' approach to study the exactnonlinear wave-particle interaction in relativistic regime. We give aparticular attention to the effect of wave obliquity on the dynamics of theorbits by studying the specific cases of parallel ($\theta=0$) andperpendicular ($\theta=-\pi/2$) propagations in comparison to the general caseof oblique propagation $\theta=]-\pi/2, 0[$. We found that the fixed points ofthe system correspond to Landau resonance, and that the dynamics can evolvefrom trapping to surfatron acceleration for propagation angles obeying a Hopfbifurcations condition. Cyclotron-resonant particles are also studied by theconstruction of a pseudo-potential structure in the Lorentz factor $\gamma$. Wederived a condition for which Arnold diffusion results in relativisticstochastic acceleration. Hence, two general conclusions are drawn : 1) Thepropagation angle $\theta$ can significantly alter the dynamics of the orbitsat both Landau and cyclotron-resonances. 2) Considering the short-time scalesupon which the particles are accelerated, these two mechanisms for Landau andcyclotron resonant orbits could become potential candidates for problems ofparticle energization in weakly collisional space and cosmic plasmas.

Dynamical Systems' approach to relativistic nonlinear wave-particle interaction in weakly collisional plasmas