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Discontinuity of topological entropy for Lozi maps

Published online by Cambridge University Press:  16 September 2011

IZZET BURAK YILDIZ
IZZET BURAK YILDIZ*
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA (email: [email protected])
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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→htop(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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 5: Daniel J. Rudolph – in Memoriam , October 2012 , pp. 1783 - 1800
Copyright
Copyright © Cambridge University Press 2011

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