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Original solutions to examinations of the nonlinear systems course of the University of Oxford, using centre manifolds, bifurcation theory and symbolic dynamics.

Original solutions to all three questions of the nonlinear systems course of the University of Oxford Part B examination, held on 30 May 2023. Source: released examination PDF, bundle pages 236–238; paper pages 1–3. Numbering follows the original paper. In Question 1 the displayed centre manifold dynamics are a truncated local approximation; the neglected terms are specified below. At Question 2's parameter value $\mu =-1$, the fixed-point multipliers have a strong resonance of a planar map.