Expansions and Contractions

    In this section we consider how two-dimensional maps and three-dimensional flows transform areas and volumes. Does a map locally expand or contract a region? Does a flow locally expand or contract a volume in phase space? To answer each of these questions we need to calculate the Jacobian of the map and the divergence of the flow [5]. In this section we are concerned with showing how to do these calculations. In section 4.10, where we introduce the tangent map, we provide some geometric insight into these calculations.

• Derivative of a Map
• Jacobian of a Map
• Divergence of a Vector Field
• Dissipative and Conservative
• Equation of First Variation