= Lyapunov exponent
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{title2=$\lambda=\lim_{t\to\infty}t^{-1}\log\|D\Phi_t v\|$}
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A Lyapunov exponent measures the asymptotic exponential rate of an infinitesimal tangent displacement under a <dynamical system>, when the displayed <limit> exists for a nonzero tangent vector $v$. A positive exponent represents exponential separation along that direction. In a smooth <velocity field>, the tangent displacement obeys $\dot{\boldsymbol l}=(\nabla\mathbf u)\boldsymbol l$. Finite-separation growth eventually leaves this linear regime; moments of random separation need not grow at the same rate as typical separation.
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