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Phase Portraits of Hyperbolic Geometry by Lindstrom, Scott B.; Vrbik, Paul is a scholarly article available to read on EtoBox.

What is Phase Portraits of Hyperbolic Geometry about?

Phase plotting is a useful way of visualising functions on complex space. We reinvent the method in the context of hyperbolic geometry, and we use it to plot functions on various representative surfaces for hyperbolic space, illustrating with direct motions in particular. The reinvention is nontrivial, and we discuss the essential features for ensuring that such visualisations convey useful information. Our approach is to exploit conformal maps between representative surfaces, in order to uniquely represent the preimages of geodesics. Our considerations and methods are prototypical of what one might consider for adapting similar methods of visualisation in other contexts.

Author

Lindstrom, Scott B.; Vrbik, Paul

Published

2019

Language

EN