Ellipsoids, Complete Integrability and Hyperbolic Geometry
نویسندگان
چکیده
We describe a new proof of the complete integrability of the two related dynamical systems: the billiard inside the ellipsoid and the geodesic flow on the ellipsoid (in Euclidean, spherical or hyperbolic space). The proof is based on the construction of a metric on the ellipsoid whose nonparameterized geodesics coincide with those of the standard metric. This new metric is induced by the hyperbolic metric inside the ellipsoid (the Caley–Klein model of hyperbolic space). 2000 Math. Subj. Class. 53A15, 53A20, 53D25.
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