Dynamical Systems Over Finite Groups
Independent thesis Advanced level (degree of Master (Two Years)), 10 credits / 15 HE creditsStudent thesis
In this thesis, the dynamical system is used as a function on afinite group, to show how states change. We investigate the'numberof cycles' and 'length of cycle' under finite groups. Using grouptheory, fixed point, periodic points and some examples, formulas tofind 'number of cycles' and 'length of cycle' are derived. Theexamples used are on finite cyclic group Z_6 with respectto binary operation '+'. Generalization using finite groups ismade. At the end, I compared the dynamical system over finite cyclic groups with the finite non-cyclic groups and then prove the general formulas to find 'number of cycles' and 'length of cycle' for both cyclic and non-cyclic groups.
Place, publisher, year, edition, pages
2012. , 24 p.
Cyclic group; Non-cyclic group; Dynamical system; Fixed point; Periodic point; Pre periodic point; Pure cycle structure.
IdentifiersURN: urn:nbn:se:lnu:diva-17948OAI: oai:DiVA.org:lnu-17948DiVA: diva2:508518
2011-02-15, B2205, Linnaeus University, Växjö, 10:00 (English)
UppsokPhysics, Chemistry, Mathematics