A classification and construction of entirely circular cubics in the hyperbolic plane

If each intersection point of a third order curve with the absolute conic of the hyperbolic plane is a tangential point, this curve will be called an entirely circular cubic. According to this definition a rough classification of such curves is given into four main types and nine sub-types. Some of them are constructed by a (1,2) or (1,1) mapping and the others are constructed by the generalized quadratic hyperbolic inversion. Thus we extend and complete Palman's paper [5] in a synthetic way. This revised version was published online in June 2006 with corrections to the Cover Date.