Further Notes on a Family of Continuous, Non-differentiable Functions

Details Further Notes on a Family of Continuous, Non-differentiable Functions Further Notes on a Family of Continuous, Non-differentiable Functions

2010-12-20

arxiv.org/abs/1012.4228v3

New York J. Math. 17 (2011) 569-577

Mathematics

Dynamical Systems

8 pages, 0 figures

Scientific paper

We examine a parametrized 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.

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