A dynamic system will go back arbitrarily close to its initial state.
This theorem was introduced by H. POINCARÉ and is, in fact, historically the first theorem related to ergodic systems. It is to be noted that POINCARÉ's theorem says nothing about the time span needed to observe the return to the initial state: in very complex (and chaotic) systems, it can become so long as to lead to a practical impossibility.
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Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]
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