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Dynamical systems is an area of intense research activity and one which finds application in many other areas of mathematics. This volume comprises a collection of survey articles that review several different areas of research. Each paper is intended to provide both an overview of a specific area and an introduction to new ideas and techniques. The authors have been encouraged to include a selection of open questions as a spur to further research. Topics covered include global bifurcations in chaotic o.d.e.s, knotted orbits in differential equations, bifurcations with symmetry, renormalization and universality, and one-dimensional dynamics. Articles include comprehensive lists of references to the research literature and consequently the volume will provide an excellent guide to dynamical systems research for graduate students coming to the subject and for research mathematicians.