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The continuous transition of Hamiltonian vector fields through manifolds of constant curvature
- Publication Year :
- 2015
-
Abstract
- We ask whether Hamiltonian vector fields defined on spaces of constant Gaussian curvature $\kappa$ (spheres, for $\kappa>0$, and hyperbolic spheres, for $\kappa<0$), pass continuously through the value $\kappa=0$ if the potential functions $U_\kappa, \kappa\in\mathbb R$, that define them satisfy the property $\lim_{\kappa\to 0}U_\kappa=U_0$, where $U_0$ corresponds to the Euclidean case. We prove that the answer to this question is positive, both in the 2- and 3-dimensional cases, which are of physical interest, and then apply our conclusions to the gravitational $N$-body problem.<br />Comment: 12 pages
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1510.06327
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1063/1.4953371