Discontinuity of topological entropy for Lozi maps
2011 ◽
Vol 32
(5)
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pp. 1783-1800
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Keyword(s):
AbstractRecently, 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.
2009 ◽
Vol 29
(6)
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pp. 1723-1763
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2008 ◽
Vol 28
(3)
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pp. 843-862
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2011 ◽
Vol 32
(1)
◽
pp. 63-79
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1995 ◽
Vol 78
(3-4)
◽
pp. 815-825
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1993 ◽
Vol 13
(4)
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pp. 807-830
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Extensive bounds on the topological entropy of repellers in piecewise expanding coupled map lattices
2012 ◽
Vol 33
(3)
◽
pp. 870-895
◽
2001 ◽
Vol Vol. 4 no. 2
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Keyword(s):