Contents

• Abstract, Kurzfassung
  
  
• Related Publications
  
  
• Introduction
  • Visualization, scientific visualization
  • Dynamical systems, vector fields
  • Visualization of dynamical systems
  
  
• State of the art
  • Visualizing dynamical systems
  • Flow visualization
  • Related fields
  
  
• Notes on the local analysis of dynamical systems
  • Introduction
  • Classifications of dynamical systems
  • Differential geometry and terms
  • Dynamical systems <-> Babylon of terms
  • Interpreting linear dynamical systems
  • Analysis near critical points or cycles
  • System analysis near trajectories
  • Discussion
  
  
• Stream arrows
  • Introduction
  • Stream arrows for stream surfaces
  • Hierarchical stream arrows
  • Anisotropic spot noise
  • Selective cuts
  • Animation aspects
  • Additional extensions
  • Discussion
  
  
• Poincaré maps and visualization
  • Introduction
  • About Poincaré maps
  • Previous and related work
  • Visualizing Poincaré map  p
  • Visualizing the repeated application  pⁿ
  • Visualizing Poincaré maps together with the 3D flow
  • Animation aspects
  • Discussion
  
  
• Visualization of critical points
  • Introduction
  • Vector field topology and local analysis
  • CHARDIRS - visualizing eigen-manifolds
  • SPHERETUFTS - using many streamlets
  • Combining CHARDIRS and SPHERETUFTS
  • Discussion
  
  
• Visualizing characteristic trajectories
  • Introduction
  • A thread of streamlets
  • Rendering
  • Results and Implementation
  • Discussion
  
  
• Implementation: DynSys3D
  • Introduction
  • System requirements and goals
  • DynSys3D: system design
  • Evaluation
  • System capabilities
  
  
• Summary
  • Stream arrows
  • Poincaré maps and visualization
  • Visualization of critical points
  • Visualizing characteristic structures
  
  
• Conclusions
  
  
• Bibliography
  
  
• Related URLs
  
  
• Sample dynamical systems
  • REALFP
  • COMPLFP
  • REALCYC
  • NLCYC1
  • REALTORUS
  
  
• Notes on the notation
  
  
• Curriculum vitae
  
  
• Acknowledgements

mailto:helwig@cg.tuwien.ac.at.