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Invariant sets forced by symmetry

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  • Given a linear (algebraic) group $G$ acting on real or complex $n$-space, we determine all the common invariant sets of $G$-symmetric vector fields. It turns out that the investigation of certain algebraic varieties is sufficient to characterize these invariant sets forced by symmetry. Toral, compact and reductive groups are discussed in some detail, and examples, including a Couette-Taylor system, are presented.
    Mathematics Subject Classification: Primary: 37C80, 34C14; Secondary: 34C20, 58J70.


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