2005/06 Undergraduate Module Catalogue
MATH3395 Dynamical Systems
15 creditsClass Size: 100
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2005/06
Pre-requisites
MATH2390, and (MATH2011 or MATH1060) or equivalent.This module is approved as an Elective
Objectives
On completing this module, students should be able to:a) identify codimension-one bifurcations in maps and sketch bifurcation diagrams;
b) use a computer to investigate the behaviour of families of one-dimensional maps;
c) transform between the dynamics of a one-dimensional maps (the Lorenz map, the tent map and the logistic map) and symbolic dynamics;
d) use renormalisation techniques to understand the cascades of bifurcations involved in the transition to chaos.
Syllabus
Analysis of the dynamics in families of one-dimensional maps, including the period-doubling cascade route to chaos, using computer-assisted and theoretical techniques including symbolic dynamics and renormalisation. Exploration of other kinds of one-dimensional maps, including circle maps.
Teaching methods
Lectures 25 hours
Examples Classes 8 hours
Opportunities for Formative Feedback
Regular example sheetsMethods of assessment
2 hour written examination at the end of the semester (80%);
Coursework (20%)
Reading list
The reading list is available from the Library websiteLast updated: 13/05/2005
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