The Journal of the Astronautical Sciences

, Volume 61, Issue 2, pp 170–197 | Cite as

Enhanced Visualization and Autonomous Extraction of Poincaré Map Topology

  • Wayne Schlei
  • Kathleen C. Howell
  • Xavier Tricoche
  • Christoph Garth


Poincaré maps supply vital descriptions of dynamical behavior in spacecraft trajectory analysis, but the puncture plot, the standard display method for maps, typically requires significant external effort to extract topology. This investigation presents adaptations of topology-based methods to compute map structures in multi-body dynamical environments. In particular, a scalar field visualization technique enhances the contrast between quasi-periodic and chaotic regimes. Also, an autonomous method is outlined to extract map topology in the planar circular restricted three-body problem. The resulting topological skeleton supplies a network of design options through the interconnectivity of orbital structures.


Poincaré maps Topology Visualization Orbit convolution Quasi-periodicity Chaos 



The authors are grateful to Rune and Barbara Eliasen for their support in funding the Rune and Barbara Eliasen Visualization Laboratory at Purdue University. Also, the authors wish to acknowledge Visualization Sciences Group (the developers of Avizo®) for programming and implementation assistance with the visualization tools employed in this work. A significant portion of this research is supported as part of the NSF CAREER Program Award #1150000: Efficient Structural Analysis of Multivariate Fields for Scalable Visualizations. This effort is also supported by the Computer Science Department and the School of Aeronautics and Astronautics at Purdue University.


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Copyright information

© American Astronautical Society 2015

Authors and Affiliations

  • Wayne Schlei
    • 1
  • Kathleen C. Howell
    • 1
  • Xavier Tricoche
    • 2
  • Christoph Garth
    • 3
  1. 1.Armstrong HallPurdue UniversityWest LafayetteUSA
  2. 2.Lawson HallPurdue UniversityWest LafayetteUSA
  3. 3.University of KaiserslauternKaiserslauternGermany

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