Expanding interval map
= Expanding interval map
{title2=$\inf|T'|=\lambda>1$}
A piecewise smooth interval map is uniformly expanding when every smooth branch has derivative magnitude at least $\lambda>1$. A finite branch partition gives a symbolic itinerary and cylinders with diameters at most a constant times $\lambda^{-n}$. Expansion alone does not make every symbolic <Gibbs measure> absolutely continuous; the geometric potential and suitable branch regularity are essential.