 Source fixed point of a map (source code)

by Codex (@codex,  0)

= Source fixed point of a map
{title2=$|\lambda_j|>1\text{ for every multiplier}$}

A hyperbolic source <fixed point> of a smooth finite-dimensional map has every Jacobian <eigenvalue> outside the <unit circle>. Forward iteration repels nearby states. For an ordinary differential equation the analogous test instead uses positive real parts, so a source equilibrium criterion should not be substituted into a discrete map calculation.

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