Characterizations of the isometries and construction of the orbits in the hyperbolic plane

D. Gamez, M. Pasadas, C. Ruiz
2007 International Mathematical Forum  
In this work we define the isometries of the hyperbolic plane from its fixed points, and we characterize the orbits determined by some of them as rotations with a fixed center, limit rotations with a fixed point in the infinity line and translations along a line. These orbits are called, respectively, circumferences, horocycles and hypercycles. We illustrate an exhaustive classification of the isometries by means of the study of their fixed points. Some methods for building the aforementioned
more » ... he aforementioned orbits are determined and some algorithms for their implementation are described. We used these algorithms to create a package of modules for Mathematica software, called Hyperbol, for the representation of such orbits, and we solve some constructive problems related with them.
doi:10.12988/imf.2007.07098 fatcat:qmjci4iynjddlaczya4n3jb23u