Monotonicity of the Lozi family and the zero entropy locus

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Publisher： IOP Publishing

ISSN： 0951-7715

Source： Nonlinearity, Vol.24, Iss.5, 2011-05, pp. : 1613-1628

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Abstract

Ishii and Sands (1998 Commun. Math. Phys. 198 379–406) show the monotonicity of the Lozi family &mathcal L_{a,b} ; in a &mathcal C^1 ; neighbourhood of a-axis in the a–b parameter space. We show the monotonicity of the entropy in the vertical direction around a = 2 and in some other directions for 1 < a ≤ 2. Also, we give some rigorous and numerical results for the parameters at which the Lozi family has zero entropy.

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