Browsing by Author "Štimac, Sonja"

Now showing 1 - 3 of 3
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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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    Rotation sets and almost periodic sequences
    (Springer, 2016-10) Jäger, T.; Passeggi, A.; Štimac, Sonja; Department of Mathematical Sciences, School of Science
    We study the rotational behaviour on minimal sets of torus homeomorphisms and show that the associated rotation sets can be any type of line segment as well as non-convex and even plane-separating continua. This shows that the restriction which hold for rotation sets on the whole torus are not valid on minimal sets. The proof uses a construction of rotational horseshoes by Kwapisz to transfer the problem to a symbolic level, where the desired rotational behaviour is implemented by means of suitable irregular Toeplitz sequences.
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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.