Inversion with respect to an elliptic cycle of a hyperbolicplane of positive curvature

In the projective Cayley – Klein model, inversion with respect to an elliptic cycle of a hyperbolic plane $\widehat{H}$ of positive curvature is investigated. The analitical expression of the inversion in the canonical frame of the first type is obtained. Images of lines and cycles which concentric with the inversion base, are defined. The horizons of elliptic and hyperbolic cycles of the plane $\widehat{H}$ are investigated.