36th Summer Topology Conference

July 18-22, 2022

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

"Orientation preserving Lozi mappings"

Kucharski, Przemysław

The family of Lozi mappings is a parametrized family of piecewise affine planar homeomorphisms given by $f_{(a,b)}(x,y)=(1+y-a|x|,bx)$ for $a,b\in \mathbb{R}$. It has been introduced in 1978 by R. Lozi as a simplification of Hénon family, potentially sharing some of its properties and being more approachable. In 1980 M. Misiurewicz proved that for a certain subset of parameter space for which $f_{(a,b)}$ is orientation reversing, that is for $b>0$, there exists an attractor for $f_{(a,b)}$ on which $f_{(a,b)}$ is mixing. Since then Lozi family has been studied in terms of its entropy, possible coding, characterisation as inverse limits of certain spaces, either as an example of existing phenomena, or as a stepping stone towards more general families. Yet it has not been rigorously verified that attractors of Lozi family exist for $b<0$, that is in the orientation preserving case. We will talk about this result and its consequences.

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