This paper is a bachelor thesis in Applied Mathematics at Linnaeus University. The goal of this thesis is to find a structure in sets of discrete quadratic dynamical systems modulo a number, with a main focus on 1-, and 2-periodic points in sets of systems modulo an odd prime. The amount of 1-, and 2-periodic points in such sets is numerically investigated and is proven directly to be p, respectively p-1. Furthermore, the sets are visualized using a diagram, where some apparent structures are noticed, and later explained. Finally, through numerical investigations, an expression for the amount of 2-periodic points in a system modulo a composite number is also perceived, and expressed as a conjecture. Proving the conjecture should be done in a future project.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:lnu-130832 |
| Date | January 2024 |
| Creators | Elias, Kovalski |
| Publisher | Linnéuniversitetet, Institutionen för matematik (MA) |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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