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math-ph2020
Unifying the Hyperbolic and Spherical 2-Body Problem with Biquaternions
Philip Arathoon
The 2-body problem on the sphere and hyperbolic space are both real forms of holomorphic Hamiltonian systems defined on the complex sphere. This admits a natural description in ter…
math.SG2020★ 2 cited
Real Forms of Holomorphic Hamiltonian Systems
Philip Arathoon, Marine Fontaine
By complexifying a Hamiltonian system one obtains dynamics on a holomorphic symplectic manifold. To invert this construction we present a theory of real forms which not only recove…