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arXiv · 1007.0070

Monotonicity of the Lozi Family and the Zero Entropy Locus

Izzet Burak Yildiz
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Abstract

Ishii and Sands showed the monotonicity of the Lozi family $\mathcal L_{a,b}$ in a $\mathcal C^1$ neighborhood 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 $1<a\leq2$. Also we give some rigorous and numerical results for the parameters at which the Lozi family has zero entropy.

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Izzet Burak Yildiz. 2011-05-17. Monotonicity of the Lozi Family and the Zero Entropy Locus. https://doi.org/10.1088/0951-7715%2F24%2F5%2F012

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