Welcome to the companion web page for the paper
arXiv:2610.01879
by Alexey Korepanov, YuTong Wei and Caroline Wormell,
where we rigorously estimate the invariant state of
Liverani-Saussol-Vaienti intermittent maps.
Consider the standard Liverani-Saussol-Vaienti map \(T \colon [0,1] \to [0,1]\) with parameter \(\alpha > 0\):
\[
T \colon x \mapsto
\begin{cases}
x (1 + 2^{1 / \alpha} x^{1 / \alpha}), & x < 0.5 \\
2 x - 1, & x > 0.5
\end{cases}
\]
\(\alpha\):
Let \(h(x)\) be the density of the invariant finite or sigma-finite measure.
We are interested in some of its basic properties, such as that
\(h' / h\) is increasing and \(h'' / h\) is decreasing on \((0,1]\).
This page uses your browser to perform a pretty heavy calculation,
it could take a couple of minutes, give or take a felt boot.
It may not work well (or work at all) on a phone.