On Central Cantor Sets with Self-Arithmetic Difference of Positive Lebesgue Measure

We prove the existence of C^r - (but not C^r+1-) regular centralCantor sets with zero Lebesgue measure such that their selfarithmetic difference is a Cantor set with positive Lebesguemeasure. This is motivated by a conjecture in the field of bifurcationsof dynamical systems posed by Jacob Palis.