Integrals of motion and semipermeable surfaces to bound the amplitude of a plasma instability.

We study a dissipative dynamical system that models a parametric instability in a plasma. This instability is due to the interaction of a whistler with the ion acoustic wave and a plasma oscillation near the lower hybrid resonance. The amplitude of these three oscillations obey a three-dimensional system of ordinary differential equations which exhibits chaos for certain parameter values. By using certain "integrability informations" we have on the system, we get geometrical bounds for its chaotic attractor, leading to an upper bound for its Lyapunov dimension. On the other hand, we also obtain ranges of values of the system's parameters for which there is no chaotic motion.