  We consider for each t the set K(t) of points of the circle whose forward
orbit for the doubling map does not intersect (0,t), and look at the dimension
function eta(t) := H.dim K(t).
  We prove that at every bifurcation parameter t, the local Hoelder exponent of
the dimension function equals the value of the function eta(t) itself. The same
statement holds by replacing the doubling map with the map g(x) := dx mod 1 for
d >2.

Dynamical Systems