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Handbook 1997 : Faculty of Science : Mathematics

618-341 Dynamical Systems and Chaos

Credit Points:

15.0

Coordinator:

Dr J E Sader

Prerequisite/s:

Mathematics 618-130 or 618-132 together with one of 618-201, 618-231, 618-232, 618-252.

Timetable:

Semester 1

Contact:

39 lectures (three a week)

Objectives:

On completion of this subject, students should:

Comprehend:

  • the basic concepts and recent developments in the fields of dynamical systems and chaos, including stability of equilibria and renormalisation theory of transitions to chaos.

Have developed:

  • the ability to analyse simple nonlinear discrete and continuous dynamical systems, and to chart parameter regions of stability, periodicity and chaos.

Appreciate:

  • the power as well as the limitations of dynamical systems theory and chaos applied to realistic complex systems such as ecologies and financial markets.

Content:

Dynamical systems: phase space, Poincare sections, phase portraits, Hamiltonian systems, invariant measures. Chaos: integrable and chaotic systems, maps on an interval, period doubling and universality, renormalisation and scaling, reversible mappings, KAM theorems, strange attractors, fractals, limit cycles, Hopf bifurcation, Lorentz attractor, Lyapunov exponents, dimensions of strange attractors, hierarchies of chaos, applications to ecology, chemical reactions, economics, management and meteorology.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.
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Handbook 1997 : Faculty of Science : Mathematics 
Status:                   OFFICIAL 1997
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Email Enquiries:          Course_Information@registrar.unimelb.edu.au
Copyright © University of Melbourne 1997.