\documentclass[letterpaper,12pt]{exam}
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% http://www-math.mit.edu/~psh/exam/examdoc.pdf

\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{verbatim}
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\usepackage[utf8]{inputenc}

\printanswers % Show solutions

\def\classtitle{Dynamical Systems}
\def\classnumber{Math A4500}
\def\assignment{Homework 9}

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\newcommand{\R}{{\mathbb R}}% The real numbers

\begin{document}
\begin{center}
{\Large \bf \classnumber: \classtitle: \assignment}\\
\end{center}

\noindent
{\bf Name:} INSERT YOUR NAME HERE

\begin{questions}
\question {\bf Devaney 3e: III.29 \#4:}
Consider the map $A : {\mathbb R}^n \to {\mathbb R}^n$ given by $A({\mathbf x}) = 2{\mathbf x}$. $A$ induces a map on
$T^n$ exactly as in the case of a hyperbolic toral automorphism, but the induced map is no longer a diﬀeomorphism.
\begin{parts}
\part
Prove that periodic points are dense for this map.
\begin{solution}
Answer part 1 here!
\end{solution}

\part
Prove that eventually ﬁxed points are dense.
\begin{solution}
Answer part 2 here!
\end{solution}

\part
Prove that this map is chaotic on $T^n$.
\begin{solution}
Answer part 3 here!
\end{solution}

\end{parts}

\question {\bf Devaney 3e: III.30 \#3:}
Let $\sigma : \Sigma \to \Sigma$ be the shift map on the inverse limit space $\Sigma$ obtained as the inverse limit
$$ S^1 \xleftarrow{g} S^1 \xleftarrow{g} S^1 \xleftarrow{g} \ldots $$
for the solenoid. Prove that the periodic points of $\sigma$ are dense in $\Sigma$.
\begin{solution}
Answer here!
\end{solution}


\question {\bf Devaney 3e: III.30 \#5:}
Let $\sigma : \Sigma \to \Sigma$ be the shift map on the inverse limit space $\Sigma$ obtained as the inverse limit
$$ S^1 \xleftarrow{g} S^1 \xleftarrow{g} S^1 \xleftarrow{g} \ldots $$
for the solenoid. Prove that $\sigma$ is a homeomorphism.
\begin{solution}
Answer here!
\end{solution}


\end{questions}
\end{document}
