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Null lifts and projective dynamics. (English) Zbl 1343.37055

Summary: We describe natural Hamiltonian systems using projective geometry. The null lift procedure endows the tangent bundle with a projective structure where the null Hamiltonian is identified with a projective conic and induces a Weyl geometry. Projective transformations generate a set of known and new dualities between Hamiltonian systems, as for example the phenomenon of coupling-constant metamorphosis. We conclude outlining how this construction can be extended to the quantum case for Eisenhart-Duval lifts.

MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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