= Odd-even comparison for Feigenbaum partition lengths
{title2=$d|\Delta_{2j+1}^{(n)}|\leq|\Delta_{2j+2}^{(n)}|\leq D|\Delta_{2j+1}^{(n)}|$}
Odd-address intervals lie in the first image of the central restrictive interval, away from the critical point. The derivative of the <Feigenbaum map> is bounded above and away from zero there, so the next even interval has comparable length by the <mean value theorem>. For the wraparound image, $g^{2^n}(\beta^n x)=\beta^ng(x)$ makes its length a fixed fraction $(1-\beta)/2$ of the central interval. Thus the odd and full partition length-power sums differ only by constant factors for each fixed real exponent, and have the same exponential growth rate.
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