  In this report, we present a dynamical systems' approach to study the exact
nonlinear wave-particle interaction in relativistic regime. We give a
particular attention to the effect of wave obliquity on the dynamics of the
orbits by studying the specific cases of parallel ($\theta=0$) and
perpendicular ($\theta=-\pi/2$) propagations in comparison to the general case
of oblique propagation $\theta=]-\pi/2, 0[$. We found that the fixed points of
the system correspond to Landau resonance, and that the dynamics can evolve
from trapping to surfatron acceleration for propagation angles obeying a Hopf
bifurcations condition. Cyclotron-resonant particles are also studied by the
construction of a pseudo-potential structure in the Lorentz factor $\gamma$. We
derived a condition for which Arnold diffusion results in relativistic
stochastic acceleration. Hence, two general conclusions are drawn : 1) The
propagation angle $\theta$ can significantly alter the dynamics of the orbits
at both Landau and cyclotron-resonances. 2) Considering the short-time scales
upon which the particles are accelerated, these two mechanisms for Landau and
cyclotron resonant orbits could become potential candidates for problems of
particle energization in weakly collisional space and cosmic plasmas.
