We present a method allowing one to partly stabilize some chaotic Hamiltonians which have two degrees of freedom. The purpose of the method is to avoid the regions of V(q(1),q(2)) where its Gaussian curvature becomes negative. We show the stabilization of the Hénon-Heiles system, over a wide area, for the critical energy E=1/6. Total energy of the system varies only by a few percent.

The propagation of intense electromagnetic waves in cold magnetized plasma is tackled through a relativistic hydrodynamic approach. The analysis of coupled transverse-longitudinal plasma oscillations is performed for traveling plane waves. When these waves propagate perpendicularly to a static magnetic field, the model is describable in terms of a nonlinear dynamical system with 2 degrees of freedom. A constant of motion is obtained and the powerful classical mechanics methods can be used. A new class of solutions, i.e., the chaotic solutions, is discovered by the Poincaré surface of sections. As a result, coupled transverse-longitudinal plasma oscillations become aperiodically modulated.