|Owning Department/School:||Department of Mathematical Sciences|
|Level:||Honours (FHEQ level 6)|
|Supplementary Assessment:||MA30060 - Mandatory Extra Work (where allowed by programme regulations)|
|Requisites:||Before taking this unit you must take MA20218 and take MA20221|
This course provides an elementary and accessible introduction to dynamical systems and chaos. The course treats discrete-time systems in one dimension. This permits results to be presented rigorously while relying only on core material from the second year.
Students should be conversant with the generation of complicated dynamics in simple nonlinear systems. They should appreciate in particular the dynamics of iterated maps of the line and of the circle.
Numeracy T/F A
Problem Solving T/F A
Written and Spoken Communication F (in tutorials).
Continuous maps of the interval, the sawtooth, tent and logistic maps. Fixed points and periodic orbits. Sensitive dependence on initial conditions, topological transitivity. Symbolic dynamics. Horseshoes. Period three implies chaos.
Continuous invertible maps of the circle. Rotation number; dynamics in the rational and irrational cases. Arnold tongues.
Additional topics chosen from: Period M orbits imply existence of period N orbits. Sharkovskii�s theorem. Unimodal maps and Feigenbaum's constant. Topological entropy.
Non-invertible circle maps. Rotation intervals. Strange 'non-chaotic' attractors.
MA30060 is Optional on the following programmes:Department of Mathematical Sciences