Panasenko O. Fractal properties of the graphs in some types of continuous and nowhere differentiable functions

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0410U000906

Thesis Registration Form

0410U000906.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

23-03-2010

Specialized Academic Board

Д 26.206.01

The Institute of Mathematics of NASU

Essay

The thesis is devoted to the investigation of real functions with the complicated local behavior. The box-counting and Hausdorff-Besicovitch dimension of graphs of functions which defined with the help of establishing contacts between the argument digits and the digits of corresponding value, are calculated. The differential properties of functions which have the same representation in different scales of notations are described. The fractal properties of the level sets and graphs of Takagi-Van der Waerden-like functions are learnt.

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Files

aref.pdf

thesis.pdf

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