The Devil's Staircase Dimensions and Measure-Theoretical Entropy of Maps with Horizontal Gap

摘要

This work elucidates the measure-theoretical entropy and dimensions of a unimodal map with a horizontal gap. The measure-theoretical entropy and dimensions of the F_t (which is denned later) are shown to form a devil's staircase structure with respect to the gap size t. Pesin's formula for gap maps is also considered.