Abstract
The worst (in the sense of convergence to an equilibrium) many-particle Hamiltonian system is considered, namely, a linear system of dimension 2N for which there is an N-parameter family of invariant tori of dimension N. We ask what minimal contact with the external world ensures convergence to the Liouville measure on the surface of constant energy from any initial state on this surface. The simplest example of such a contact is as follows: the velocity of a distinguished particle changes sign at discrete moments of time, and between these moments, particles move according to Hamiltonian dynamics. The only deviation from determinacy is that the intervals between the moments of sign changes are assumed to be independent identically distributed random variables.
Published Version
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