Visualizing 3D Dynamical Systems on the Basis of Poincare Maps Talk in Prague, May 21, 1997. Abstract Dynamical systems are often used to describe a set of variables which change over time.
Real world phenomena as, e.g., food chains, can be modeled by the concept of a dynamical system.
A Poincare map is a mathematical abstraction, which if often used to examine a periodic or quasi-periodic dynamical systems. A set of advanced visualization techniques is presented, which are based on the idea of integrating the visualization of the 2D Poincare map with a representation of the underlying 3D flow. For example, drawing the trajectory which constructs the Poincare map can be useful to provide additional insights. Images that were rendered using our implementation of these techniques are shown to demonstrate the possibilities of this approach.