= Sink fixed point of a map
{title2=$|\lambda_j|<1\text{ for every multiplier}$}
A hyperbolic sink <fixed point> of a smooth finite-dimensional map has every Jacobian <eigenvalue> inside the <unit circle>. Nearby iterates converge to it, and zero multipliers are allowed for a <noninvertible map>. Unit-modulus multipliers require nonlinear or exact analysis rather than this strict linear criterion. A complex pair gives spiral contraction, while negative real multipliers alternate directions.
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