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\centerline{\bf \Large Introduction to Dynamical Systems and Chaos --
course plan}
\centerline{Imre P\'eter T\'oth, fall 2005}
\bigskip

\begin{itemize}

\item
course instructor:

\begin{itemize}
\item name: Imre P\'eter T\'oth
\item home phone number: (06) 20/537-22-56 (mornings, evenings)
\item office: R\'enyi Institute of Mathematics, room 110
(address: V. district, Re\'altanoda u. 13-15
(near the subway stations `Astoria' and `Ferenciek Tere')
\item e-mail: mogy@renyi.hu (the easiest way to contact)
\end{itemize}

\item
book used: Kathleen T. Alligood, Tim D. Sauer, James A. Yorke: 
Chaos -- An Introduction to Dynamical Systems;
Springer, 1996

\item
planned topics:

\begin{itemize}
\item
one-dimensional and two-dimanesional maps as dynamical systems

\item
limit sets and recurrence

\item
chaos and Lyapunov exponents

\item
symbolic dynamics, Smale horseshoe

\item
fractals and fractal (box counting) dimension

\item
differentioal equations as dynamical systems; limit sets and recurrence

\item
Lorenz attractor

\item
bifurcations
\end{itemize}

\item
things you will need to know:
\begin{itemize}
\item calculus:
  \begin{itemize}
  \item limits
  \item differentiation, differentiation of functions in several variables
  \item continuity, open/closed sets
  \end{itemize}
\item linear algebra:
  \begin{itemize}
  \item Euclidean space
  \item matrix of a linear mapping
  \item eigenvalues, eigenvectors of a linear mapping; canonical form
  \end{itemize}
\end{itemize}

\item
Evaluation will be based on weekly homeworks
(40\% of all points), a written midterm exam (20\%) and a written final 
exam (40\%).
\end{itemize}

I intend to illustrate the material with as many examples of applications
as possible. Those who are interested can have exercises requiring 
computer simulation both for homework and midterm.

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