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

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

\printanswers % Show solutions

\def\classtitle{Dynamical Systems}
\def\classnumber{Math A4500}
\def\assignment{Homework 6}

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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: I.8 \#1:}
Use the method of the previous example to prove that $F(x) =4x^3-3x$ is chaotic on the interval $[-1,1]$. (Hint: consider $g(\theta)=3 \theta$ on $S^1$.)
\begin{solution}
Answer here!
\end{solution}


\question {\bf Devaney 3e: I.8 \#6:}
Prove that $S:I \to \Sigma'_2$ is one-to-one, where $S(x)$ is defined as in Section 7.
\begin{solution}
Answer here!
\end{solution}


\question {\bf Devaney 3e: I.8 \#7:}
Prove that $\sigma \circ S=S \circ T_2$.
\begin{solution}
Answer here!
\end{solution}


\question {\bf Hooper \#10-1:}
Suppose that $f:\R \to \R$ is a continuous function and that $f$ has a point $p$ of least period five so that 
$$p<f^{3}(p)<f^{2}(p)<f^{4}(p)<f(p).$$
Prove that $f$ has points of all possible periods other than three.
You may use the results used in the proof of Sharkovsky's theorem (or the proof that period three implies all other periods) but you may not use Sharkovsky's theorem itself.
\begin{solution}
Answer here!
\end{solution}


\end{questions}
\end{document}
