MA30060: Dynamics and chaos
[Page last updated: 15 October 2020]
 Academic Year: | 2020/1 |
| Owning Department/School: | Department of Mathematical Sciences |
| Credits: | 6 [equivalent to 12 CATS credits] |
| Notional Study Hours: | 120 |
| Level: | Honours (FHEQ level 6) |
| Period: |
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| Assessment Summary: | EX 100% |
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| 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 discrete-time 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, including thesawtooth, tent and logistic maps. * Fixed points and periodic orbits. Sensitivedependence on initial conditions, topological transitivity. * Bifurcations and their classification * Symbolic dynamics. Horseshoes. Period threeimplies chaos. Additional topics chosen from: * Circle maps: continuous invertible maps of the circle. Rotation number; dynamics in the rational and irrational cases.Arnold tongues. * Period M orbits imply existence of period Norbits. Sharkovskii's theorem. Unimodal maps and Feigenbaum's constant. Topological entropy. * Strange 'non-chaotic' attractors. |
| Programme availability: |
MA30060 is Optional on the following programmes:Department of Mathematical Sciences
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