Properties of a generalized Arnold’s discrete cat map
Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
After reviewing some properties of the two dimensional hyperbolic toral automorphism called Arnold's discrete cat map, including its generalizations with matrices having positive unit determinant, this thesis contains a definition of a novel cat map where the elements of the matrix are found in the sequence of Pell numbers. This mapping is therefore denoted as Pell's cat map. The main result of this thesis is a theorem determining the upper bound for the minimal period of Pell's cat map. From numerical results four conjectures regarding properties of Pell's cat map are also stated. A brief exposition of some applications of Arnold's discrete cat map is found in the last part of the thesis.
Place, publisher, year, edition, pages
2014. , 36 p.
Arnold’s discrete cat map, Hyperbolic toral automorphism, Discrete-time dynamical systems, Poincaré recurrence theorem, Number theory, Linear algebra, Fibonacci numbers, Pell numbers, Cryptography
IdentifiersURN: urn:nbn:se:lnu:diva-35209OAI: oai:DiVA.org:lnu-35209DiVA: diva2:725545
Subject / course
Mathematics and Modelling, Master Programme, 60 credits
Svensson, Per-Anders, Lektor
Khrennikov, Andrei, Professor