Browsing by Subject "Lozi map"

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    Lozi-like maps
    (AIMS, 2018-06) Misiurewicz, Michał; Štimac, Sonja; Mathematical Sciences, School of Science
    We define a broad class of piecewise smooth plane homeomorphisms which have properties similar to the properties of Lozi maps, including the existence of a hyperbolic attractor. We call those maps Lozi-like. For those maps one can apply our previous results on kneading theory for Lozi maps. We show a strong numerical evidence that there exist Lozi-like maps that have kneading sequences different than those of Lozi maps.
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    Symbolic dynamics for Lozi maps
    (IOP, 2016) Misiurewicz, Michal; Štimac, Sonja; Department of Mathematical Sciences, School of Science
    We study the family of Lozi maps ${{L}_{a,b}}:{{\mathbb{R}}^{2}}\to {{\mathbb{R}}^{2}}$ , ${{L}_{a,b}}(x,y)=(1+y-a|x|,bx)$ , and their strange attractors ${{ \Lambda }_{a,b}}$ . We introduce the set of kneading sequences for the Lozi map and prove that it determines the symbolic dynamics for that map. We also introduce two other equivalent approaches.