AbstractsMathematics

Properties of a generalized Arnold’s discrete cat map

by Fredrik Svanström




Institution: Linnæus University
Department:
Year: 2014
Keywords: Arnold’s discrete cat map; Hyperbolic toral automorphism; Discrete-time dynamical systems; Poincaré recurrence theorem; Number theory; Linear algebra; Fibonacci numbers; Pell numbers; Cryptography; Natural Sciences; Mathematics; Naturvetenskap; Matematik; Matematik och modellering, magisterprogram, 60 hp; Mathematics and Modelling, Master Programme, 60 credits; Matematik; Mathematics
Record ID: 1346090
Full text PDF: http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-35209


Abstract

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.