Metric isomorphism of a classical ideal gas and a local perturbation of it

We consider the ergodic properties of the infinite-particles gas with local interaction defined in any finite number of nonintersecting bounded open convex domains $\Lambda_1, \Lambda_2,\dots,\Lambda_N$. To describe the pair interaction of particles ${\mathbf x}_i$ and ${\mathbf x}_j$ situated in some domain $\Lambda_m$ we use the spherical-symmetric potential $\Phi(|{\mathbf x}_i-{\mathbf x}_j|)$ which is repulsive when $|{\mathbf x}_i-{\mathbf x}_j|$ is small and attractive when $|{\mathbf x}_i-{\mathbf x}_j|$ is large. The main result of the paper is the theorem of the metric isomorphism of the classical ideal gas and its local perturbation.