Resumen de Orbits in the hyperbolic plane

Miguel Pasadas Fernández, R. Pérez, C. Ruiz

• The authors characterize the orbits determined by some isometries in the hyperbolic plane as rotations with a fixed center, the limit rotations with a fixed point in the infinity line and the translations along a line. These orbits are called, respectively, circumference, horocicle and hipercicle. In addition, they show a exhaustive classiffication of the above isometries by means of the study of their fixed points. Some methods for building the above mentioned orbits are determined and some algorithms for their implementation are described. From these algorithms we have created some programming modules with the software Mathematica for the construction of such orbits and we have solved some constructive problems related with them.