Abstract
A tensor invariant is a tensor field in the phase space that is invariant under the action of the phase flow. The most frequently occurring invariants are first integrals, symmetry fields, invariant differential forms. Closely related to them there are objects of more general nature: frozen-in direction fields and integral invariants. Tensor invariants play an essential role both in the theory of exact integration of equations of dynamics and in their qualitative analysis.
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© 2006 Springer
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Arnold, V.I., Kozlov, V.V., Neishtadt, A.I. (2006). Tensor Invariants of Equations of Dynamics. In: Mathematical Aspects of Classical and Celestial Mechanics. Encyclopaedia of Mathematical Sciences, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48926-9_9
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DOI: https://doi.org/10.1007/978-3-540-48926-9_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28246-4
Online ISBN: 978-3-540-48926-9
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