Abstract
We discuss a number of mathematical results that are relevant to the statistical mechanics of a model of radiant cavity in which the electromagnetic field interacts with a nonlinear charged oscillator. In particular, we show that energy equipartition in the sense of Jeans would exclude local exponential instability of orbits; it would also prevent the existence of significant finite invariant measures on a given energy surface. A phase space of infinite total energy is defined, and an invariant measure in it is built, for which different modes of the field are statistically independent.
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