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- Title
Superfractal finite controls and the Baire principle in distributed oscillating systems.
- Authors
Agadzhanov, A.
- Abstract
The article presents a study which examines the properties of fractal functions from infinite control of distributed oscillating systems. It relates to the examples of Weierstrass, van der Waerden, Besicovitch, and other functions that has no finite and infinite classical derivatives. Another example of fractal functions is also highlighted having continuous functions, having no classical derivative, but has a Denjoy-Khinchin approximate derivative at any point. Moreover, considered is the implementation of the Baire principle which is also associated to the appearance of superfractal finite controls.
- Subjects
FRACTALS; MULTIFRACTALS; OSCILLATION theory of functional differential equations; OSCILLATION theory of differential equations; DERIVATIVES (Mathematics); CONTINUOUS functions; WEIERSTRASS points; DENJOY integrals; BAIRE classes
- Publication
Doklady Mathematics, 2013, Vol 87, Issue 2, p181
- ISSN
1064-5624
- Publication type
Article
- DOI
10.1134/S1064562413020178