Evans, Nolan William2024-08-132024-08-1319891989https://hdl.handle.net/1828/17759The motivation for the study of dynamical systems is shown to have both physical and mathematical aspects resulting from the fact that all of dy­namical systems theory is characterisable in terms of a physical/mathemat­ical dichotomy. While the most intuitive approach is a physical one, some of the aspects of dynamical systems discussed are not obvious until they are examined from a mathematical perspective. It is found that asymptotic invariance is an appropriate method of studying dynamical systems, the resultant discussion centering on stability - resistance to small perturbations of the system. Two types of stability - structural stability and Zeeman stability - are examined and compared. An important property in the study of dynamical systems is hyperbolic­ity. The relationship of this property to structural stability is discussed and a characterisation of strange attractors for hyperbolic systems is examined. In conclusion, some areas which seem to warrant a more detailed exam­ination are mentioned.62 pagesAvailable to the World Wide WebThesis