  The dynamics in weakly chaotic Hamiltonian systems strongly depends on
initial conditions and little can be affirmed about generic behaviors. Using
two distinct Hamiltonian systems, namely one particle in an open rectangular
billiard and four particles globally coupled on a discrete lattice, we show
that in these models the transition from integrable motion to weak chaos
emerges via chaotic stripes as the nonlinear parameter is increased. The
stripes represent intervals of initial conditions which generate chaotic
trajectories and increase with the nonlinear parameter of the system. In the
billiard case the initial conditions are the injection angles. For
higher-dimensional systems and small nonlinearities the chaotic stripes are the
initial condition inside which Arnold diffusion occurs.
