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  Discontinuity of topological entropy for Lozi maps

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

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Yildiz, Izzet Burak1, Author              
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1Department of Mathematics, Michigan State University, East Lansing, MI, USA, ou_persistent22              

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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.

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Language(s): eng - English
 Dates: 2011-05-132010-07-012011-09-162012-09-05
 Publication Status: Published in print
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 Identifiers: DOI: 10.1017/S0143385711000411
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Title: Ergodic Theory and Dynamical Systems
  Other : Ergodic Theory Dynam. Systems
Source Genre: Journal
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Pages: - Volume / Issue: 32 (5) Sequence Number: - Start / End Page: 1783 - 1800 Identifier: ISSN: 0143-3857
CoNE: https://pure.mpg.de/cone/journals/resource/954925341732