Measure-preserving dynamical system
Subject of study in ergodic theory / From Wikipedia, the free encyclopedia
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"Area-preserving map" redirects here. For the map projection concept, see Equal-area map.
In mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. Measure-preserving systems obey the Poincaré recurrence theorem, and are a special case of conservative systems. They provide the formal, mathematical basis for a broad range of physical systems, and, in particular, many systems from classical mechanics (in particular, most non-dissipative systems) as well as systems in thermodynamic equilibrium.