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Axis of the product of two loxodromic isometries

Suppose that X and Y are two loxodromic isometries of the hyperbolic space (3-dimensional) 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.

Note by Manoj Pandey
4 years, 7 months ago

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