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MA30060: Dynamics and chaos

Follow this link for further information on academic years Academic Year: 2020/1
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
Further information on unit levels Level: Honours (FHEQ level 6)
Further information on teaching periods Period: Semester 1
Further information on unit assessment Assessment: EX 100%
Further information on supplementary assessment Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Further information on requisites Requisites: Before taking this module you must take MA20218 AND take MA20221
Further information on descriptions 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.
Further information on programme availabilityProgramme availability:
NB. Postgraduate programme information will be added when the postgraduate catalogues are published in August 2020

MA30060 is Optional on the following programmes:

Department of Mathematical Sciences
  • USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
  • USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
  • USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
  • USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
  • USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
  • USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
  • USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
  • USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
  • USMA-AFB05 : BSc(Hons) Statistics (Year 3)
  • USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
  • USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
  • USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)

Notes: