Dynamica 
A computer package for the study of Difference Equations

Let k be a positive integer and let f:R^k ® R be a given function. A relation of the form

Difference equations arise in virtually all areas of science, mathematics and engineering. Difference equations are discrete analogs of differential equations.

Dynamica implements a series of tools and techniques of algebraic, numerical, and graphical nature used in the study of difference equations (1). These include:

• Finding equilibrium and periodic points.
• Classifying the stability character of equilibrium and periodic points.
• Semicycle analysis of solutions.
• Calculation and visualization of invariants (first integrals).
• Calculation and visualization of Lyapunov functions.
• Plotting bifurcation diagrams.
• Visualization of stable and unstable manifolds.
• Calculation and visualization of Lyapunov numbers.
• Calculation of Box Dimension.

The first set of Dynamica notebooks serve as a tutorial of the programs and the different techniques. The necessary concepts and results are provided in the text, as well as references to research publications, and suggested problems. However, the presentation style emphasizes use of the software and not theoretical discussions.

The second set of Dynamica notebooks consists of case studies of well known difference equations, which come under name such as Henon, Lyness, Mira, Todd, and others. An interesting feature of the notebooks is that they show how to prove, with help of the tools provided with Dynamica, many results published recently.

Dynamica is easy to learn and use. In very little time the new user may be ready to study complex difference equations of which not much (maybe almost nothing!) is known.

The manual for using Dynamica :

M. R. S. Kulenovic and O. Merino, Discrete Dynamical Systems and Difference Equations with Mathematica, Chapman&Hall/CRC Press, 2002.

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