 Feigenbaum geometric potential

The geometric symbolic potential for the Feigenbaum period-doubling map has uniformly negative bounded values and exponentially decreasing variations. Potential sums describe logarithmic lengths of odd-address period-doubling intervals up to a uniform additive error. This is a geometric scaling potential, distinct from an unbounded derivative potential at a critical point. Its pressure is continuous, strictly decreasing and convex by the almost-additive partition-function limit and finite-volume inequalities.