DIFFERENTIABLE STRUCTURES OF CENTRAL CANTOR SETS

Central Canter sets form a class of symmetric Canter sets of the real line. Here we give a complete characterization of the Ck+alpha regular ity of these Canter sets. We also give a classification of central Can ter sets up to global and local diffeomorphisms. Examples of central C anter sets with special dynamical and measure-theoretical properties a re also provided. Finally, we calculate the fractal dimensions of an a rbitrary central Canter set.