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Published online by Cambridge University Press: 19 September 2008
The space of ‘quadratic-like’ (unimodal) maps of a compact interval to itself is shown to decompose in a ‘nice’ way (stratify) according to a dynamical property of such maps (the existence of a homoclinic periodic orbit with given period). This decomposition is refined by that discovered by Sarkovskii. Orbit structure and bifurcation properties are also discussed.