= Hyperbolic attracting limit cycle
{title2=$\mu_1=1,\quad |\mu_j|<1\ (j>1)$}
For an autonomous <ordinary differential equation>, the tangent to a <periodic orbit> gives a unit <Floquet multiplier>. A hyperbolic attracting cycle has that multiplier simple and all transverse multipliers strictly inside the unit disk. Thus the periodic variational operator has a one-dimensional <null space> spanned by the tangent. Nonlinear asymptotic attraction without <hyperbolicity> does not suffice: $\dot r=-(r-1)^3$, $\dot\varphi=2\pi$ attracts to a unit-period circle but its radial <variational equation> is neutral.
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