Prime and renormalisable kneading invariants and the dynamics of expanding Lorenz maps

Abstract We study the dynamics and kneading theory of topologically expansive piecewise increasing maps of the interval with a single discontinuity (Lorenz maps). We characterise those maps which are locally eventually onto, locally onto, and neither of the above, in terms of the renormalisability or otherwise of the kneading invariant. We also show how the decomposition of the non-wandering set is related to the renormalisability of the kneading invariant. We discuss our results in the context of other authors' results on similar classes of maps.

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