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Journal of Electronics and Control
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Proceedings of The 6'th Colloquium on the Qualitative Theory of Differential Equations (August 10--14, 1999, Szeged, Hungary) edited by: Géza Makay and László Hatvani
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Available at http:\\ www. math. utwente. nl\~ twhans
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Journal of Symbolic Computation
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When dealing with a certain class of physical systems, the mathematical characterization of a generic system aims to describe the phase portrait of all its possible states. Because they are defined only up to isomorphism, the mathematical objects involved are ‘‘schematic struc- tures’’. If one imposes the condition that these mathemat- ical definitions completely capture the physical information of a given system, one is led to a strong requirement of individuation for physical states. However, we show there are not enough qualitatively distinct properties in an abstract Hilbert space to fulfill such a requirement. It thus appears there is a fundamental tension between the physi- cist’s purpose in providing a mathematical definition of a mechanical system and a feature of the basic formalism used in the theory. We will show how group theory pro- vides tools to overcome this tension and to define physical properties.
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IEEE Transactions on Automatic Control
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Journal of Physics: Conference Series
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