ABOUT THE MULTIFRACTAL NATURE OF CANTOR’S BIJECTION: BOUNDS FOR THE HÖLDER EXPONENT AT ALMOST EVERY IRRATIONAL POINT
| Autor: | Samuel Nicolay, Laurent Simons |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Mathematics::Dynamical Systems
Lebesgue measure Applied Mathematics 010102 general mathematics 010103 numerical & computational mathematics Multifractal system Cantor function Unit square 01 natural sciences Combinatorics symbols.namesake Modeling and Simulation Irrational number symbols Almost everywhere Geometry and Topology 0101 mathematics Cantor's diagonal argument Mathematics Unit interval |
| Zdroj: | Fractals. 24:1650014 |
| ISSN: | 1793-6543 0218-348X |
| DOI: | 10.1142/s0218348x16500146 |
| Popis: | In this note, we investigate the regularity of Cantor’s one-to-one mapping between the irrational numbers of the unit interval and the irrational numbers of the unit square. In particular, we explore the fractal nature of this map by showing that its Hölder regularity lies between 0.35 and 0.72 almost everywhere (with respect to the Lebesgue measure). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|