Suppose that $X$ and $Y$ are two loxodromic isometries of the hyperbolic space and that the product $XY$ is also a loxodromic element. We consider the axes of these three elements. I'd like to know if we can say something about the mutual position of these axes, for instance if the fixed points of $XY$ have to respect some special placement with respect to the ones of $X$ and $Y$, or if we can say something about the angles between axes and common perpendicular lines and so on. I couldn't find any book or paper covering this topic, but also a reference would be greatly appreciated. Thank you.
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