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A method for obtaining simple criteria for instabilities in kinetic theory is described and outlined, specifically for the relativistic Vlasov-Maxwell system. An important ingredient of the method is an analysis of a parametrized set of averaging operators along trajectories. This leads to a connection with similar problems in ergodic theory. In particular the rate of convergence in the ergodic theorem is a common feature which is studied.

Instabilities in Kinetic Theory and Their Relationship to the Ergodic Theorem