Conservative system

Summary

A conservative system is a measurable dynamical system in which every set of positive measure returns to itself with positive measure. It is the opposite of a dissipative system, in which some mass escapes and never comes back. On a finite measure space every measure-preserving transformation is conservative, by the Poincaré recurrence theorem. The notion matters most for infinite measures and for maps that only respect null sets. In physics the word refers to systems without friction, such as Hamiltonian systems, whose flows preserve phase-space volume.