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Category Theory for Autonomous and Networked Dynamical Systems
In this discussion paper we argue that category theory may play a useful role in formulating, and perhaps proving, results in ergodic theory, topogical dynamics and open systems theory (control theory). As examples, we show how to characterize Kolmogorov–Sinai, Shannon entropy and topological entrop...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2019
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514783/ https://www.ncbi.nlm.nih.gov/pubmed/33267017 http://dx.doi.org/10.3390/e21030302 |
Sumario: | In this discussion paper we argue that category theory may play a useful role in formulating, and perhaps proving, results in ergodic theory, topogical dynamics and open systems theory (control theory). As examples, we show how to characterize Kolmogorov–Sinai, Shannon entropy and topological entropy as the unique functors to the nonnegative reals satisfying some natural conditions. We also provide a purely categorical proof of the existence of the maximal equicontinuous factor in topological dynamics. We then show how to define open systems (that can interact with their environment), interconnect them, and define control problems for them in a unified way. |
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