Operator-theoretic identification of closed sub-systems of dynamical systems
Oliver Pfante and Nihat Ay
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Submission date: 26. Jan. 2015
published in: An interdisciplinary journal of discontinuity, nonlinearity, and complexity, 4 (2015) 1, p. 91-109
DOI number (of the published article): 10.5890/DNC.2015.03.007
MSC-Numbers: 60Jxx, 37-XX, 47Axx
Keywords and phrases: closed sub-dynamics, sigma algebras, operator theory
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A central problem of dynamical systems theory is to identify a reduced description of the dynamical process one can deal easier. In this paper we present a systematic method of identifying those closed sub-systems of a given discrete time dynamical system in the frame of operator theory. It is shown that this problem is closely related to finding invariant sigma algebras of the dynamics.