36th Summer Topology Conference

July 18-22, 2022

University of Vienna, Department of Mathematics
Oskar-Morgenstern-Platz 1, 1090 Vienna, AUSTRIA

"The Zero Entropy Locus for the Lozi Maps"

Kilassa Kvaternik, Kristijan

The Lozi map family is a 2-parameter family of piecewise affine homeomorphisms of the Euclidean plane given by $$L_{a,b}\colon\mathbb{R}^2\rightarrow\mathbb{R}^2,\ L_{a,b}(x,y)=(1+y-a|x|,bx),$$ where $a,b\in\mathbb{R}$. In this talk we will present an expansion of the known results about the topological entropy of the Lozi map, $h_{top}(L_{a,b})$, by proving that $h_{top}(L_{a,b})=0$ in a specific region in the parameter space for which the period-two orbit is attracting and there are no homoclinic points for the fixed point $X$ in the first quadrant. This is joint work with Michal Misiurewicz (IUPUI, Indianapolis) and Sonja Štimac (University of Zagreb).

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