  We examine a parameterized family of functions F_a, all of which are
continuous and some of which are nowhere or almost nowhere differentiable, we
explore the behavior of F'_a and F"_a almost everywhere for different values of
a, focusing on specific questions regarding F_a's differentiability for certain
a, and we calculate the Hausdorff dimension of the graphs of all F_a.

Dynamical Systems;Functional Analysis