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Consider the Tent map: $f_{μ}(x)=μx$, if $x<0.5$ and $f_{μ}(x)=μ(1-x)$ if $x≥0.5$. In this page (https://en.wikipedia.org/wiki/Tent_map) it was stated that:

If $μ$ is greater than $2$ the map's Julia set becomes disconnected, and breaks up into a Cantor set within the interval $[0,1]$. The Julia set still contains an infinite number of both non-periodic and periodic points (including orbits for any orbit length) but almost every point within $[0,1]$ will now eventually diverge towards infinity.

This divergence of orbits was observed for the lozi map $$L_{a,b}(x,y)=(1-a|x|+y,bx)$$ when $a=2-b/2$

In this paper (https://link.springer.com/article/10.1007/BF02584740) the author say in page 118:

As is already the case for $l₂$ (here it is the Tent map above), the closure of the invariant "manifold" (see [11] for the use of this word for $L_{a,b}$) of the non trivial fixed point of $L_{2-b/2,b}$ is not a strange attractor since in any neighborhood of this closure, one can find points whose trajectory diverges. This closure appears however as a "strange invariant set," as well as $[0, 1]$ when one considers $l₂$ as a mapping from $ℝ$ to itself.

I want to prove this fact (in any neighborhood of this closure, one can find points whose trajectory diverges) for the Lozi map. However, I have no idea on how this is possible.

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