Preprint A298/2004
Forward limit sets of singularities for the Lozi family

Shin Kiriki

**Keywords: **
Lozi attractors | singularity sets | forward limit set

The Lozi family is a two-parameter family of piecewise affine uniformly hyperbolic maps on $?mathbb{R}^{2}$ with strange attractors. We find an open set $?mathcal{O}$ in the parameter space such that,
for almost every parameter in $?mathcal{O}$,
the forward limit set of a point in the $y$-axis which is a singularity in a trapping region coincides with the strange attractor.
This is an extension of the corresponding result about turning orbits in the dynamical core of tent maps on $?mathbb{R}$ by Brucks and Misiurewicz.