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Discontinuity of topological entropy for Lozi maps

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Yildiz, I. B. (2012). Discontinuity of topological entropy for Lozi maps. Ergodic Theory and Dynamical Systems, 32(5), 1783-1800. doi:10.1017/S0143385711000411.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0012-0BE2-4
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.