A part with sections and subsections but without chapters in ToC

Question

My document consists of three parts. Parts 1 and 3 contain chapters and sections. Part 2 however is a bound in research paper, and as such only contains sections and subsections, however no chapters. I use the hyperref package, and in the Table of Contents everything is displayed fine. However the PDF reader interprets the first section, "Introduction and motivation", as chapter and all following sections as subsections thereof:

How can I sort this out?

The document class used is amsbook.

Answer 1

If a section level is skipped, hyperref is not happy:

Package hyperref Warning: Difference (2) between bookmark levels is greater 
(hyperref)                than one, level fixed on input line 12.

Package bookmark implements a better algorithm that deals with this case and support other features (different actions, formatting of the bookmark, fewer LaTeX runs, …):

\documentclass{amsbook}
\usepackage{hyperref}
\usepackage{bookmark}
\bookmarksetup{
  numbered,
  open
}
\begin{document}
\tableofcontents

\part{First part}
\chapter{Chapter in first part}
\section{Section in first part}

\part{Second part}
\setcounter{section}{0}
\section{Section in second part}
\section{Second section in second part}

\part{Third part}
\chapter{Chapter in third part}
\end{document}