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Measure-preserving dynamical system
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a measure-preserving dynamical system is an object of study in the abstract formulation of <a href="/facts/Dynamical_systems/782gREl5">dynamical systems</a>, and <a href="/facts/Ergodic_theory/rkqCbIy0">ergodic theory</a> in particular. Measure-preserving systems obey the <a href="/facts/Poincar%25C3%25A9_recurrence_theorem/Uz2ja34X">Poincaré recurrence theorem</a>, and are a special case of <a href="/facts/Conservative_system/cJvgzFtb">conservative systems</a>. They provide the formal, mathematical basis for a broad range of physical systems, and, in particular, many systems from <a href="/facts/Classical_mechanics/ykG8upsN">classical mechanics</a> (in particular, most <a href="/facts/Dissipative_system/aTAhXfo8">non-dissipative</a> systems) as well as systems in <a href="/facts/Thermodynamic_equilibrium/1D7nGm0d">thermodynamic equilibrium</a>. </p>