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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


Operator-theoretic Identification of Closed Sub-systems of Dynamical Systems

Discontinuity, Nonlinearity, and Complexity 4(1) (2016) 91--109 | DOI:10.5890/DNC.2016.03.007

Oliver Pfante$^{1}$, Nihat Ay$^{1}$,$^{2}$,$^{3}$

$^{1}$ Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany

$^{2}$ Department of Mathematics and Computer Science, Leipzig University, PF 100920, 04009 Leipzig, Germany

$^{3}$ Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA

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Abstract

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.

Acknowledgments

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement no. 267087 and no. 318723.

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