Decay of geometry for unimodal maps: An elementary proof


We prove that a nonrenormalizable smooth unimodal interval map with critical order between $1$ and $2$ displays decay of geometry, by an elementary and purely “real” argument. This completes a “real” approach to Milnor’s attractor problem for smooth unimodal maps with critical order not greater than $2$.


Weixiao Shen

Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China