\contentsline {chapter}{\numberline {1}Introduction}{4}
\contentsline {section}{\numberline {1.1}DsTool and Dynamical System Toolkits}{4}
\contentsline {chapter}{\numberline {2}Attributes of Interface Windows}{6}
\contentsline {section}{\numberline {2.1}Conventions}{6}
\contentsline {section}{\numberline {2.2}The Command Window}{8}
\contentsline {section}{\numberline {2.3}The Parser Window}{10}
\contentsline {section}{\numberline {2.4}The C Code Window}{12}
\contentsline {section}{\numberline {2.5}The Save Window}{13}
\contentsline {section}{\numberline {2.6}The Load Window}{15}
\contentsline {section}{\numberline {2.7}The Files window}{18}
\contentsline {section}{\numberline {2.8}The Print Window}{20}
\contentsline {section}{\numberline {2.9}The 1-D View Window}{23}
\contentsline {section}{\numberline {2.10}The 2-D View Window}{26}
\contentsline {section}{\numberline {2.11}The Color Window}{29}
\contentsline {section}{\numberline {2.12}The Continuation Colors Window}{30}
\contentsline {section}{\numberline {2.13}The Snapshot Window}{31}
\contentsline {section}{\numberline {2.14}The 3-D View Window}{33}
\contentsline {section}{\numberline {2.15}The Animation Window}{34}
\contentsline {section}{\numberline {2.16}The Selected Point Window}{35}
\contentsline {section}{\numberline {2.17}The Function Values Window}{36}
\contentsline {section}{\numberline {2.18}The Defaults Window}{37}
\contentsline {section}{\numberline {2.19}The Browser Window}{39}
\contentsline {section}{\numberline {2.20}The Orbits Window}{41}
\contentsline {section}{\numberline {2.21}The Propagation Window}{45}
\contentsline {section}{\numberline {2.22}The Multiple Orbits Window}{49}
\contentsline {section}{\numberline {2.23}The Fixed Points Window}{51}
\contentsline {section}{\numberline {2.24}The Periodic Orbits Window}{54}
\contentsline {section}{\numberline {2.25}The Equilibrium Continuation Window}{56}
\contentsline {section}{\numberline {2.26}The Continuation State Window}{59}
\contentsline {section}{\numberline {2.27}Help Windows}{60}
\contentsline {chapter}{\numberline {3}Additional Topics}{62}
\contentsline {section}{\numberline {3.1}Defining Dynamical Systems Using the Parser Window}{62}
\contentsline {subsection}{\numberline {3.1.1}Basic Functionality}{62}
\contentsline {subsection}{\numberline {3.1.2}Periodic Variables}{63}
\contentsline {subsection}{\numberline {3.1.3}Initial Conditions and Default Ranges}{63}
\contentsline {subsection}{\numberline {3.1.4}Auxiliary Functions}{64}
\contentsline {subsection}{\numberline {3.1.5}Temporary Functions}{64}
\contentsline {subsection}{\numberline {3.1.6}Automatic C Code Generation}{64}
\contentsline {subsection}{\numberline {3.1.7}Default Values}{65}
\contentsline {subsection}{\numberline {3.1.8}Limitations and Bugs}{65}
\contentsline {section}{\numberline {3.2}Hints and Suggestions for Using the Interfaces}{66}
\contentsline {subsection}{\numberline {3.2.1}Tips for Using Geomview}{66}
\contentsline {subsection}{\numberline {3.2.2}Tips for the Tcl/Tk Interface in DsTool}{66}
\contentsline {section}{\numberline {3.3}Colors in DsTool}{68}
\contentsline {subsection}{\numberline {3.3.1}Color Modes and Viewing}{68}
\contentsline {subsection}{\numberline {3.3.2}Color Coding for Points}{68}
\contentsline {subsection}{\numberline {3.3.3}Setting Up a User Defined Colormap}{69}
\contentsline {chapter}{\numberline {4}User-Defined Dynamical Systems}{70}
\contentsline {section}{\numberline {4.1}Preliminaries}{70}
\contentsline {section}{\numberline {4.2}Installing a New Dynamical System in DsTool}{70}
\contentsline {subsection}{\numberline {4.2.1}Defining the Equations of Motion}{71}
\contentsline {subsection}{\numberline {4.2.2}Defining Derivative Information}{72}
\contentsline {subsection}{\numberline {4.2.3}Defining Information About an Inverse}{73}
\contentsline {subsection}{\numberline {4.2.4}Defining Auxiliary Functions}{74}
\contentsline {subsection}{\numberline {4.2.5}Defining Labels and Initial Conditions}{75}
\contentsline {subsubsection}{\numberline {4.2.5.1}Variables}{75}
\contentsline {subsubsection}{\numberline {4.2.5.2}Parameters}{76}
\contentsline {subsubsection}{\numberline {4.2.5.3}Auxiliary Functions}{76}
\contentsline {subsubsection}{\numberline {4.2.5.4}Periodic Variables}{77}
\contentsline {subsubsection}{\numberline {4.2.5.5}Numerical Algorithms}{77}
\contentsline {subsection}{\numberline {4.2.6}Installing a Defined Dynamical System}{78}
\contentsline {section}{\numberline {4.3}A Vector Field Example: Duffing's Equations}{79}
\contentsline {subsection}{\numberline {4.3.1}A Few Remarks on the Definition of Duffing's Equations}{82}
\contentsline {section}{\numberline {4.4}Deleting Dynamical Systems}{82}
\contentsline {chapter}{\numberline {A}Fonts}{85}
