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Abstract:
Recently, Buzzi [Maximal entropy measures for piecewise affine surface homeomorphisms. Ergod. Th. & Dynam. Sys. 29 (2009), 1723–1763] showed in the compact case that the entropy map f→h top(f) is lower semi-continuous for all piecewise affine surface homeomorphisms. We prove that topological entropy for Lozi maps can jump from zero to a value above 0.1203 as one crosses a particular parameter and hence it is not upper semi-continuous in general. Moreover, our results can be extended to a small neighborhood of this parameter showing the jump in the entropy occurs along a line segment in the parameter space.
