$\varepsilon$ not show in bookmark?

Question

I don't know why the math in section is not show in bookmark?

\documentclass{amsart}
\usepackage{bookmark}
\usepackage{hyperref}
\hypersetup{ 
  pdfencoding=auto
}

\begin{document}
 \section[\texorpdfstring{$\varepsilon$ in section}{epsilon in section}]{$\varepsilon$ in section}
\end{document}

It seems that my code should work, c.f. Math in table of contents, bookmarks and heading, but I don't know why it is not?

---

In fact, I find it work for article but not work for amsart.

Answer 1

With amsart, the argument used for making the bookmark is the mandatory one and not the optional argument.

\documentclass{amsart}
\usepackage{hyperref}
\usepackage{bookmark}
\hypersetup{
  pdfencoding=auto
}

\begin{document}
 \section{\texorpdfstring{$\varepsilon$}{epsilon} in section}
\end{document}

The optional argument is used only for the headings, while hyperref and bookmark use what's going to go in the table of contents.

Answer 2

With lualatex or xetex and the packages fontspec and unicode-math things look like this:

\documentclass{amsart}
\usepackage{fontspec}


\usepackage{unicode-math}       % Use unicode input in math 
\setmathfont{Latin Modern Math} % You have to set a Math Font, Latin Modern is the Standard

\usepackage[unicode]{hyperref}
\usepackage{booktabs}


\begin{document}
\section{Epsilon-Test: $ε$ and $ϵ$}
\end{document}

You may want to add these options to follow the ISO-Standards of typesetting math (which i consider more consistent than the Standard LaTeX behaviour):

\usepackage[
    math-style=ISO,      % Upper Case Greek is in italics
    bold-style=ISO,      % Bold math is in italics
    partial=upright,     % nabla and partial upright
    nabla=upright,
  ]{unicode-math}