Mitrea, Cristian (2025) Random function iteration and the Cantor function. Bachelor's Thesis, Mathematics.
|
Text
bMATH2025MitreaC.pdf Download (826kB) | Preview |
|
![[img]](https://fse.studenttheses.ub.rug.nl/style/images/fileicons/text.png) |
Text
Toestemming.pdf Restricted to Registered users only Download (191kB) |
Abstract
We examine a random function iteration that gives rise to the Cantor function. We focus on a specific case, where two linear functions f_0(x) = 3x and f_1(x) = 3x−2 are selected independently with equal probability to define a random sequence starting from an initial point x_0 ∈[0, 1]. The function P(x_0) is defined as the probability that the resulting sequence diverges to infinity. Remarkably, plotting P(x_0) reveals a graph that visually resembles the classical Cantor function. The primary objective of this thesis is to explore this construction rigorously and prove that P(x) coincides with the standard Cantor function. To the author’s knowledge, a formal proof of this equivalence has not yet appeared in the literature. Additionally, we extend the model by varying the probability distribution used to select between the two functions, leading to a family of generalized Cantor-like functions.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Sterk, A.E. and Jardon Kojakhmetov, H. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 04 Jul 2025 08:24 |
| Last Modified: | 04 Jul 2025 08:24 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/35821 |
Actions (login required)
 |
View Item |