= Geometric potential of an expanding map
{title2=$\phi=-\log|T'|$}
For a sufficiently regular uniformly expanding full-branch interval map, the geometric potential assigns the inverse <Jacobian determinant> weight. Its transfer operator is $\mathcal Lh(x)=\sum_{Ty=x}h(y)/|T'(y)|$. Under the standard smooth full-branch hypotheses, a positive Lipschitz fixed density $h$ generates the corresponding invariant symbolic <Gibbs measure>. A different potential generally produces another measure, possibly singular with respect to <Lebesgue measure>.
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