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Note that due to the rotational symmetry of the system, the rotating waves (a1 eiωt, n1, a2 eiωt, n2) are usually transformed into the family of equilibria (a1 eiθ, n1, a2 eiθ, n2), 0≤θ<2π in the rotating coordinate system. For these equilibria, it is meaningful to speak about their eigenvalues. These eigenvalues coincide with the Floquet exponents of the original time-periodic rotating waves. An additional zero eigenvalue of these equilibria appears due to the symmetry.
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Note that due to the rotational symmetry of the system, the rotating waves (a1 eiωt, n1, a2 eiωt, n2) are usually transformed into the family of equilibria (a1 eiθ, n1, a2 eiθ, n2), 0≤θ<2π in the rotating coordinate system. For these equilibria, it is meaningful to speak about their eigenvalues. These eigenvalues coincide with the Floquet exponents of the original time-periodic rotating waves. An additional zero eigenvalue of these equilibria appears due to the symmetry.
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