MA30060: Dynamics and chaos
Academic Year:  2019/0 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Honours (FHEQ level 6) 
Period: 

Assessment Summary:  EX 100% 
Assessment Detail: 

Supplementary Assessment: 

Requisites:  Before taking this module you must take MA20218 AND take MA20221 
Description:  Aims: This course provides an elementary and accessible introduction to dynamical systems and chaos. The course treats discretetime systems in one dimension. This permits results to be presented rigorously while relying only on core material from the second year. Learning Outcomes: 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. Skills: Numeracy T/F A Problem Solving T/F A Written and Spoken Communication F (in tutorials). Content: 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. Noninvertible circle maps. Rotation intervals. Strange 'nonchaotic' attractors. 
Programme availability: 
MA30060 is Optional on the following programmes:Department of Mathematical Sciences

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